INSTITUTE OF PHYSICS PUBLISHING MODELLING AND SIMULATION IN MATERIALS SCIENCE AND ENGINEERING

Modelling Simul. Mater. Sci. Eng. 13 (2005) 553–565 doi:10.1088/0965-0393/13/4/006

Influence of a welding sequence on the welding

residual stress of a thick plate

S D Ji, H Y Fang, X S Liu and Q G Meng

State Key Laboratory of Advanced Welding Technology Production, Harbin Institute of

Technology, Harbin 150001, People’s Republic of China

Received 26 October 2004, in final form 17 March 2005

Published 27 April 2005

Online at stacks.iop.org/MSMSE/13/553

Abstract

The residual stress in one-groove welding using an ellipsoidal heat source is

analysed. The results show that it can ameliorate the residual stress distribution

and greatly decrease the peak value of residual stress after welding if the

converse welding method is adopted between adjacent layers in a multi-layer

weld, or between adjacent beads in every layer. Moreover, the numerical

simulation results of the double V-groove thick plate welding model show

that the residual tensile stress appears on the weld and nearby, the residual

compressive stress appears on the area far away from the weld and the peak value

of tensile stress appears on the surface of the weld. Differences in the welding

sequence influence the value and the distribution of the welding residual stress

greatly, and a more suitable welding sequence can be deduced. The reliability

of the numerical simulation results is proved by the experimental results.

(Some figures in this article are in colour only in the electronic version)

1. Introduction

In the past 100 years, welding has been one of the most widely used technologies. It is very

difficult to find another technology that can develop as quickly as welding and can compare

with welding in the field of scale and diversification [1–3]. Moreover, welding plays a very

important role especially in manufacturing metal structures. The quality of welding influences

the quality of the project directly. Therefore, in order to control the quality of the metal

structure, a proper welding sequence is essential [4–9].

During the welding process, metal structure engenders distortion in some areas due to

the violent temperature change. The weld’s shrinkage in the process of cooling after welding

produces the internal stress. Thus, the welding region will cause the phenomena of jut, twist

and so on. Not only is it difficult to guarantee the dimensions of the work piece, but also the

existence of welding residual stress will reduce the rigidity and fatigue strength of the metal

structure. Therefore, it is important to construct a feasible welding sequence before welding

in order to reduce the residual stress after welding, and, thus, guarantee the welding quality of

0965-0393/05/040553+13$30.00 © 2005 IOP Publishing Ltd Printed in the UK 553

554 S D Ji et al

Figure 1. Mesh generation of finite model.

the workpiece [10–14]. During production, researchers have accumulated a lot of experience

on how to arrange the welding sequence [15–22], but the experience usually aims at a certain

concrete work piece instead of a general suitability.

The plate’s welding mainly includes one-groove welding and double-groove welding.

This paper discusses the numerical simulation of a double V-groove thick plate’s welding

residual stress by studying the influence of the welding sequence on the residual stress of

one-groove welding. A more reasonable welding sequence is obtained, and the simulation

result is compared with the experimental result obtained for the plate. Because the rational

welding sequence that results from the numerical simulation is suitable for general welding

procedures, it has important significance for practical applications.

2. Residual stress of one-groove welding

2.1. Effect of the welding direction on residual stress in multi-layer welding

2.1.1. Establishment of multi-layer welding’s finite element model. Due to the symmetry of

the workpiece, only half of the model is analysed. The dimensions of this plate model are

600mm × 400mm × 15 mm, and this model is divided into three layers to weld. The length

of an element of weld perpendicular to the welding direction is 1.25mm and the length of

an element of weld in the welding direction is 2.5 mm. The mesh is shown in figure 1. The

welding region has been subdivided and the area far away from the weld is meshed relatively

wider. This not only reduces the calculation time but guarantees computational accuracy. This

model is divided into 12420 hexahedral elements and 15656 nodes.

2.1.2. Confirmation of welding material and welding condition. In the numerical simulation,

Martensite Stainless Steel, 1Cr12NiWMoNb is chosen as the base material and filler metal.

The welding method used is GMAW. The voltage of the electric arc is 25V, the electric current

is 210A and the welding speed is 5mms−1.

2.1.3. Confirmation of the welding heat source. Because the welding method is GMAW,

the moving ellipse heat source is adopted in numerical simulations. It can be described by

Welding sequence on the welding residual stress 555

(a) (b)

(c) (d)

Figure 2. Schematic of several welding directions.

the following expression:

q(x, y, z, t) = 6

√

3Q

πabc

√

π

e−3x2/a2 e−3y2/b2 e−3[z+v(∂−t)]2/c2

.

Here, v represents the welding speed and Q the heat input rate, while a, b and c are the

dimensions of the heat source, and their values are 0.005 m, 0.005mand 0.006 m, respectively.

∂ represents the time lag of the welding heat source.

2.1.4. Taking account of the martensitic transformation. In this paper, because the material

of all models is martensitic and it undergoes transformation during the welding process, this

transformation must be considered.

In Marc, the change in heat quantity during the phase change can be controlled by latent

heat and the volumetric change during the phase change can be controlled by the coefficient

of thermal expansion. Moreover, these can be realized by a subprogram that is designed by

the author.

2.1.5. Simulation result of residual stress. Several kinds of welding directions are designed,

as is shown in figure 2. The weld is divided into three layers, and the arrows represent the

moving directions of the welding heat source.

The residual stress distribution trend of the above-mentioned welding sequences is the

same as that of the single layer welding. All the residual tensile stress appears in the weld and

nearby area, while all their peak values appear on the weld, so no figures are given here.

The equivalent Von Mises stress is a rule to judge whether the material in elastically or

plastically deformed. When the equivalent stress is lower than the material’s yielding limit,

the material is in the elastic phase; when the stress reaches its yielding limit, it can be regarded

as being in the plastic phase. So, it is important to study the equivalent stress in the process of

the numerical simulation of welding. The expression for this is as follows:

σ = 1 √

2

(σ1 − σ2)2 + (σ2 − σ3)2 + (σ1 − σ3)2.

In the expression, σ represents the equivalent Von Mises stress, while σ1, σ2 and σ3

represent the three principal stresses of one point in the plate, respectively.

Because the equivalent stress distribution trends of the above-mentioned four schemes are

all the same, the result of scheme c is taken as an example. It is shown in figure 3. The distance

in figure 3 represents the distance from one point to the centre line of the weld.

From figure 3, it can be seen that the peak value of the equivalent Von Mises stress appears

on the weld, and the equivalent stress gradually decreases to nearly zero in the area far away

from the weld.

556 S D Ji et al

Equivalent stress (MPa)

Distance (m)

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20

0

100

200

300

400

Figure 3. Equivalent stress distribution of the weld’s middle section.

Table 1. Residual stress’s peak in different welding directions in multi-layer welding.

Scheme serial number

a b c d

Equivalent stress (MPa) 546 528 422 521

Transverse stress (MPa) 453 351 336 422

Longitudinal stress (MPa) 463 363 356 431

Table 1 shows the peak values of transverse and longitudinal residual stress obtained by

the above-mentioned schemes.

It can be seen from table 1 that the third scheme (namely, the converse welding between

adjacent layers) can effectively reduce residual stress after welding.

When welding the first layer, because the area of heat emission of the striking arc region

or quenching arc region is relatively smaller, the temperature variation between these two parts

is relatively more significant than that in the weld’s middle part. Therefore, in the process of

welding, greater compressive plastic deformation is produced near the striking arc region and

near the quenching arc region than in the weld’s middle part. In the process of cooling after

welding, the striking arc region or the quenching arc region, consequently endures greater

tensile residual stress than the middle part of the weld. Moreover, because the intensity of

temperature variation on the striking or quenching arc region is different, two different peak

values appear on the two parts. When welding the second layer, if the converse welding method

is adopted, the trend of residual stress distribution is opposite to that in the first layer. Thus,

the two layers’ resultant effect makes the residual stress distribution relatively even, and then

the peak value is relatively low. This is why the converse welding method is better.

2.2. Effect of the welding direction on residual stress in multi-bead welding

The dimensions of the finite model are 200mm ×150mm ×4 mm, and the width of the weld

is 20.4 mm, which is packed with three beads. The mesh of the weld area is fine and the

gradational transition to the coarse mesh is gradually carried out. The length of an element

Welding sequence on the welding residual stress 557

Figure 4. Mesh generation of plate.

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14

0

100

200

300

400

500

Equivalent stress (MPa)

Distance (m)

Figure 5. Equivalent stress distribution of the weld’s middle section.

of weld in the welding direction is 2.5 mm. This structure is divided into 3520 hexahedral

elements and 4736 nodes, as shown in figure 4.

The welding material, the welding condition and the welding heat source of this model

are all the same as those in the multi-layer welding.

Four kinds of different welding directions are designed like multi-layer welding, as shown

in figure 2. The arrows show the welding direction of the three beads, and the bottom arrow’s

position represents the centre line of the weld.

Because the stress distribution trends of the above-mentioned four schemes are the same,

the result of scheme b is taken as an example. Figure 5 is the distribution of equivalent stress

on top of the plate and figure 6 is the distribution of longitudinal residual stress on top of the

plate. Distance in the following two figures represents the distance from one point to the centre

line of the weld.

From figure 5, it can be seen that the peak value of equivalent stress appears on the weld

and the value of stress is nearly zero in the area far away from the weld. From figure 6,

it is seen that the longitudinal residual tensile stress appears on the weld and nearby while

the compressive stress appears on the area away from the weld. Moreover, because of the

severe change in temperature at the interface between the base metal and the weld, the peak

value of tensile residual appears in this area. Because the distribution trend of transverse stress

is similar to that of longitudinal stress, it is not discussed here.

558 S D Ji et al

Longitudinal stress (MPa)

Distance (m)

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14

-300

-200

-100

0

100

200

300

400

500

Figure 6. Longitudinal residual stress distribution of the weld’s middle section.

Table 2. Peak residual stress of different welding directions in multi-bead welding.

Scheme serial number

a b c d

Equivalent stress (MPa) 602 595 561 601

Transverse stress (MPa) 500 525 489 522

Longitudinal stress (MPa) 559 552 500 551

200

150

36

14 2 20

40

Figure 7. Dimensions of the specimen for simulation in mm.

The peak values of stress of several different schemes are shown in table 2. From this

table, it can be seen that the peak values obtained from scheme c are the minimum. That is, in

multi-bead welding, the residual stress is the minimum when the converse welding method is

adopted.

3. Welding residual stress of a double V-groove thick plate

3.1. Establishment of the multi-layer welding model

Figure 7 is a model of the double V-groove plate. Figure 8 is the meshing sketch map of this

model.

The base material and filler metal material of the double V-groove welding model is

also Martensite Stainless Steel, 1Cr12NiWMoNb. The welding heat source is an ellipse heat

Welding sequence on the welding residual stress 559

Figure 8. Mesh generation of double V-groove model.

Figure 9. Schematic of weld beads’ delamination.

source model. The welding electric current is 200 A, the welding voltage is 25V, and the

welding speed is 5mms−1. Moreover, the model’s preheating temperature is 100˚C, while the

temperature between the layers is lower than 150˚C in the welding process.

In the course of numerical simulation, the weld is divided into nine layers, as shown in

figure 9. In this figure, 1, 2, 3, 4, 5, 6, 7, 8 and 9, respectively, express the serial number for

each layer of the weld.

In order to study the influence of welding sequences on residual stress, several kinds

of welding sequences are designed according to the above-mentioned weld. Moreover, the

position of each layer’s serial number represents the precedence order of each layer in the

welding process:

(a) 2 3 1 4 8 5 9 6 7;

(b) 2 3 4 1 5 8 6 9 7;

(c) 2 3 1 4 5 8 6 7 9;

(d) 1 2 8 3 9 4 5 6 7;

(e) 1 2 3 8 4 5 9 6 7;

(f) 1 2 3 8 9 4 5 6 7;

(g) 1 2 3 4 5 8 6 9 7;

(h) 2 3 4 5 1 6 8 7 9.

560 S D Ji et al

Figure 10. Distribution of equivalent stress.

Figure 11. Distribution of transverse residual stress.

3.2. Distribution of the residual stress field of the double V-groove thick plate

In each of the above-mentioned welding sequences, the distribution of residual stress is

substantially consistent. Therefore, only the residual stress of scheme f is discussed here.

Moreover, in the course of the numerical simulation, the converse welding method is adopted

between adjacent layers in a multi-layer weld or between adjacent beads in every layer.

Figure 10 shows the distribution of equivalent stress. Figure 11 shows the distribution of

the transverse residual stress, while figure 12 shows the distribution of the longitudinal residual

stress.

The following observations can be made from the figures: the peak value of equivalent

stress appears on the weld; the longitudinal or transverse residual tensile stress of the thick

plate is mainly distributed on the weld or near the weld and the peak value appears on the

weld; the longitudinal or transverse compressive residual stress appears far away from the

Welding sequence on the welding residual stress 561

Figure 12. Distribution of longitudinal residual stress.

Distance (m)

Equivalent stress (MPa)

0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040

300

350

400

450

500

550

600

650

Figure 13. Distribution of equivalent stress along the thickness of the weld in the weld’s middle

section.

weld. Moreover, because no constraint exists, the longitudinal residual stress at the two ends

of the bead approaches zero.

Figure 13 is the distribution of equivalent stress along the thickness of the thick plate on

the weld’s middle section. Figure 14 is the distribution of transverse residual stress along the

thickness while figure 15 is the distribution of longitudinal residual stress along the thickness

of the thick plate in the weld’s middle section. In the following figures, ‘Distance’ represents

the distance from the point to the bottom of the thick plate.

From these figures, it is seen that the peak values of equivalent stress, transverse residual

stress or longitudinal stress appear on the surface of the plate, while the stress value is relatively

lower in the middle part.

3.3. Experimental validation

In order to validate the simulation results, experimental verification has been carried out in the

double V-groove plate. Moreover, in order to facilitate the analysis, the scheme f is chosen

562 S D Ji et al

Distance (m)

Transverse stress (MPa)

0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040

0

50

100

150

200

250

300

350

400

450

500

550

Figure 14. Distribution of transverse stress along the thickness of the weld in the weld’s middle

section.

0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040

-200

-100

0

100

200

300

400

500

600

Distance (m)

Longitudinal stress (MPa)

Figure 15. Distribution of longitudinal stress along the thickness of the weld in the weld’s middle

section.

as the welding method. The material, the plate’s dimensions and the welding condition in the

experiment are all the same as those in the simulation.

The AST portable x-ray stress tester is adopted to test the residual stress of the specimen.

The x-ray method involves irradiating the specimen by x-rays after the specimen has been

treated, and then the diffraction is obtained. The internal stress is measured from the crystal

lattice distortion. This method is not only easy to carry out but also keeps the specimen intact.

Moreover, it is acceptable to measure surface residual stress.

Figure 16 is the contrast between the test result and the simulation result of transverse

residual stress on the surface of the plate’s middle section. Figure 17 is the contrast between

the test result and the simulation result of longitudinal residual stress on the surface of the

plate’s middle section. In these two figures, ‘Distance’ represents the distance from one point

to the centre line of the weld.

Welding sequence on the welding residual stress 563

Distance (m)

Transverse stress (MPa)

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16

-200

-100

0

100

200

300

400

500

600

Experimental result

Simulation result

Figure 16. Experimental verification of transverse residual stress.

Distance (m)

Longitudinal stress (MPa)

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16

-200

-100

0

100

200

300

400

500

600 Experimental result

Simulation result

Figure 17. Experimental verification of longitudinal residual stress.

It can be seen by analysing those two figures that the longitudinal or transverse residual

stress of simulation results is basically the same as the experimental results from the viewpoint

of changing trends. It proves that the simulation results are rational and reliable.

3.4. Simulation results of several welding sequences

Table 3 is the contrast of the residual stress’s peak values. It can be seen from the table that the

peak values of transverse residual stress or longitudinal residual stress that are obtained from

scheme c are the minimum. Therefore, this welding sequence is reasonable.

Abstractly, the distribution of welding temperature is not even along the thickness direction

of the thick plate. One part of the welded plate expands more while the other part expands less

or even not at all. Therefore, the expansion of the welded part is blocked and, then, transverse

564 S D Ji et al

Table 3. Residual stress’s peak value for several schemes.

Scheme serial number

a b c d e f g h

Equivalent stress (MPa) 701 712 571 885 653 658 921 912

Transverse stress (MPa) 623 544 405 718 505 511 829 857

Longitudinal stress (MPa) 634 636 507 823 592 607 879 865

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20

-400

-200

0

200

400

600

Welding in same direction

Welding in inverse direction

Distance (m )

Transverse stress (MPa)

Figure 18. Comparison of transverse stress between welding in the same direction and welding in

the inverse direction.

compressive plastic deformation is generated. What is more, because of the phenomenon of

uneven shrinkage along the thickness direction of the plate after welding, angular deformation

appears on the workpiece and then the root of the weld carries high tensile stress. When the

tensile stress resulting from the welding angular deformation exceeds the tensile strength’s

critical value of the filler metal in the root of the weld, a crack appears on the weakest root of

the weld. Therefore, when the filler metal of the weld is more uniformly filled, the angular

deformation is less and then the residual stress is less. This is why the residual stress that is

obtained by scheme c is the minimum.

In order to validate whether the welding residual stress that is obtained by the converse

welding method between adjacent layers is the minimum, the double V-groove plate’s welding

stress is studied under the condition of synclastic welding or converse welding. The contrast

in welding transverse residual stress is shown as in figure 18, and ‘Distance’ in figure 18

represents the distance between points and the endpoint of the weld. The simulation result

shows that the peak value of the welding transverse residual stress by the method of converse

welding is 405.4MPa, which is 18.2% less than the stress by the method of synclastic welding.

Moreover, the contrast of the longitudinal stress is similar to this figure and the stress’s peak

value decreases by 16.9%.

4. Conclusions

(1) The simulation results of the plate butt welding show that the peak values of transverse

residual tensile stress and longitudinal residual tensile stress obtained by the method of

Welding sequence on the welding residual stress 565

converse welding between adjacent layers in a multi-layer weld, or between adjacent

beads in every layer, are the minimum. Therefore, the residual stress in the weld is greatly

reduced if this method is adopted. The weld’s strength is enhanced and the quality is

improved.

(2) The residual stress distribution in the double V-groove thick plate shows that the residual

tensile stress appears on or near the weld and the peak value appears on the weld.

Moreover, the simulation results are validated by the experimental results.

(3) The contrast between the simulation results of a double V-groove thick plate welded using

many different welding sequences shows that differences in welding sequence affect the

distribution and the peak value of the residual stress, and also affect the strength and the

crack resistance of the weld. Moreover, a kind of suitable welding sequence is obtained

by comparing simulation results; e.g. when two parts of the weld are filled more evenly,

the residual stress is less.

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