Three Dimensional Modeling Weld Solidification Cracks

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Three dimensional modeling weld solidification cracksin multipass welding

Z.B. Dong a,*, Y.H. Wei b

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

Harbin 150001, Chinab Department of Material Science and Technology, Nanjing University of Aeronautics and Astronautics,

Nanjing 210016, China

Available online 24 August 2006

Abstract

This paper utilizes element birth and death finite element technique to control the process of filling metal step by stepduring multipass welding process. The dynamic thermal distributions and strain evolutions are simulated in 10 mmSUS310 stainless steel in multipass welding after taking into consideration of the fluid flow in the weld pool, the latentheat, taking into account the effect of the deformation in weld pool, change of initial temperature and solidification shrink-age. At the same time, the driving forces to weld solidification cracks of each weld pass are obtained successfully accordingto simulated thermal cycle (temperature against time) and mechanical strain cycle (mechanical strain against time). The

results show the patterns of distribution of the driving force are similar to those of surface fusion welding. The drivingforce of first weld pass is larger than following weld passes and the driving force decreases gradually in company with weld-ing processing. Sequent welding processes affect the mechanical strain distributions of previous weld pass, of which thetensile mechanical strain changes to compressive strain. In addition, the driving forces are analyzed and weld solidificationcracks are predicted during multipass welding. The predicted results agree well with the experiments. Therefore, the sim-ulated results in this study provide the foundation for predicting weld solidification cracking in actual weldment.Ó 2006 Elsevier Ltd. All rights reserved.

1. Introduction

Thick plates are widely not only used to jointactual welding structures in industry but also arenormally accompanied by the addition of filler mate-rial as new weld passes e.g. Manual Metal Arc(MMA) welding, Metal-Inert Gas (MIG) welding,Submerged Arc welding. Multipass welding process

is often used with taking into consideration of thelimitation of fusion width and fusion depth of single

pass welding process between the joins of thickplates. However, this makes it difficult to modelthe multipass welding with Finite Element Method(FEM). Due to the intense concentration of heat inthe heat source of welding, the regions near the weldline undergo severe thermal cycles, thereby maybegenerating weld solidification cracks in the weld-ment. Therefore, predicting three dimensional weldsolidification cracks have been a major topic in weld-ing a variety of engineering alloys.

0167-8442/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved.

doi:10.1016/j.tafmec.2006.07.007

* Corresponding author. Tel./fax: +86 451 86417650.E-mail address: [email protected] (Z.B. Dong).

Theoretical and Applied Fracture Mechanics 46 (2006) 156–165

www.elsevier.com/locate/tafmec

mailto:[email protected]

mailto:[email protected]



Full three dimensional simulation of fusionwelding process, for the purpose predicting residualstresses, is now feasible and practical, given recentdevelopments in computing capabilities. Manyresearchers have studied the thermal distributions

and residual stresses in multipass welding. Predictedin [1] are the residual stresses during multipass arcwelding in steel pipes using finite element techniquesand discussed the effects of pipe diameter and wallthickness on weld residual stresses. Adaptive meshrefinements [2] are used for a procedure to transportthe results between the different meshes. Thethermo-mechanical model used as well as the simu-lation methodology was detailed. Computed distor-tions and residual stresses were compared withexperimental measurements. Multipass circumferen-tial butt-welding is simulated [3] for stainless steel

pipes in a non-linear thermo-mechanical FE-analy-sis. In particular, the axial and hoop stresses andtheir sensitivity to variation in weld parameters werestudied. Described in [4–10] is a combined analyticaland experimental method for analyzing the residualstresses in a pipe formed with a girth-butt weld.

For the studying of weld solidification cracking,an analysis was performed [11,12] for a bead-on-plate weld for an aluminum plate and evaluatedthe mechanical strain near the weld pool. Hot-crack-ing was studied [13] for a butt-welded aluminum

plate. They assumed that the large solidificationshrinkage was compensated by refeeding from themelt until a critical strain of 2% was reached. Thisvalue was obtained by fitting simulations with exper-iments. A good agreement was obtained betweencomputed and measured locations of cracks nearthe edge of the plate. A detailed analysis was made[14] for the weld pool region as a preparation forcrack analysis observing that the computed strainswere sensitive to the high temperature properties.However, the weld metal solidification crack in mul-tipass welding was rarely studied and simulatedowing to the complex procedures involved with thesimulation, especially to structure weldments.

On the basis of simulating the single pass welding[15–17], the present investigation utilizes elementbirth and death finite element technique to controlthe process of filling metal step by step during multi-pass welding process. At the same time, the dynamicthermal distributions and strain evolutions are ana-lyzed in 10 mm plate-butt SUS310 stainless steel inmultipass welding with FEM. The driving forces toweld solidification cracks of each pass weld are

obtained successfully according to simulated ther-

mal cycle and mechanical strain cycle. The compar-ison between the calculated driving force and thematerial resistance predict the weld metal solidifica-tion cracking. Therefore, the simulated results in thisstudy provide the foundation for predicting weld

solidification cracking in actual weldment.

2. Computational model

2.1. Analysis procedure

For the model under consideration, the internalheating due to the plastic dissipation can beneglected considering the small transformation ratesgenerated by a welding operation. Therefore, anuncoupled thermal and thermo-mechanical analysisis adopted in this calculation. The thermal analysis

is performed first and the transient temperature his-tory obtained from heat transfer analysis is used asthe thermal loads for subsequent thermo-mechani-cal analysis. In the simulated results, the total strainis composed of thermal strain, elastic strain andplastic strain. The mechanical strain is obtained byelastic strain plus plastic strain.

This paper utilizes the double ellipsoidal heatsource proposed in [18] to analyze three dimensionalFE model. The process of filling metal can be trea-ted in commercial FE-codes MSC.Marc by compil-

ing specially defined user subroutines to activatenew elements in the model through so-called ‘‘ele-ment birth and death’’ finite element technique dur-ing multipass welding process.

2.2. Analysis of butt weld joint

Multiple passes are used to produce the weldbead layers in a butt weld joint. The numerical anal-ysis has multiple heat input steps to reflect the mul-tipass process. Fig. 1 shows the finite element meshof multipass welding.

Two plates of size 100 · 50 · 10 mm which wouldform a single Y -groove joint are used to simulate themultipass welding. Only one plate is discretized witheight-node isoparametric hexahedron elements dueto the symmetry along the weld center line.

Two plates to be welded are tacked together atboth ends before welding with a uniform gap of 2 mm between the plates, as it is used in industrialfabrication. The typical thermal–mechanical prop-erties of the material used are given in literature[15]. This paper takes into account the effect of the

latent heat and the fluid flow in the weld pool in

Z.B. Dong, Y.H. Wei / Theoretical and Applied Fracture Mechanics 46 (2006) 156–165 157



thermal analysis and the deformation in weld pool,change of initial temperature for thermal stress/strain calculation and solidification shrinkage areconsidered in the mechanical model. These methodscan be seen in literature [15]. The overall fillingwelds are divided into three passes and the fillingmaterials are the same as the base metal.

In the heat transfer process, heat is lost from thesurfaces in the form of convection and radiation.They occur on all surfaces of the plate except theplane of symmetry, which is defined as adiabatic.In the mechanical model, all nodes on symmetricalsurface are fixed y-displacement. The other mechan-ical boundary conditions are applied to avoid therigid body movements of the plate.

The different sets of welding parameters are adop-ted during multipass welding as shown in Table 1.

3. Results and discussion

3.1. Thermal distributions during multipass welding

After deposition of each weld pass, the model

was allowed to cool down until the maximum tem-

perature at any position along the deposited beadreached the specified inter-pass temperature foreach pass. Fig. 2 depicts the three-dimensional ther-mal distributions of different passes welding.

From Fig. 2, it can be seen that the temperature

in front of the weld molten pool is zero since the fill-ing metals are not activated. Whereas, the thermaldistributions at the back of weld molten pool areproper as well as actual welding since the activatedweld metals take part in simulating.

The thermal cycles of seven positions summa-rized in Table 2 in the model are shown inFig. 3.

It can be seen that different point has differenttime to reach the peak temperature. The time of point a, b, c, d , e and f is 30 s, 390 s, 750 s and after750 s.

Knowledge of average maximum temperaturerises will be useful in the estimation of maximumtemperatures attained by different regions of thebase plate during multipass welding. Likely changesin the microstructure and consequent degradationin mechanical properties can be estimated from thisinformation [19].

For any weld pass, the lowest and highest tem-peratures (in Fig. 3) seen by a point of simulationcan be found from the simulated results. The differ-ence (A–A 0) between these two values will give the

maximum temperature rise attained at the point of measurement during that pass. The average valueof these two maximum temperature rises will givethe average maximum temperature rise at thereferred measurement point. Similar average maxi-mum temperature rise values can be obtained forother simulated points also.

In Fig. 4, the average maximum temperature riseobtained as explained above, is plotted against dis-tance from the weld pad centre line. A similar curveis drawn in the same figure that corresponds to thefirst pass weld of the same plate.

From these curves, it can be seen that the averagemaximum temperature rise uniformly varies withdistance from the weld pad centre line. The averagemaximum temperature rise expected at any otherpoint lying between them can be read directly fromthese curves. It can be also seen that the heat energyinput for the three passes are different, as seen fromTable 1. These are 0.75 kJ/mm for pass No. 1 and1.44 kJ/mm for pass No. 2 and 2.4 kJ/mm for passNo. 3. It can be observed that for any other heatinput value between these two values, the corre-

sponding curve can be drawn by interpolation,

Fig. 1. The mesh used for multipass welding. (a) 3D mesh usedfor calculation and (b) cross-section of mesh.

Table 1Welding parameters during multipass welding

Passnumber

Weldingvoltage (V)

Weldingcurrent (A)

Speed(mm/s)

1 20 60 1.62 24 120 23 24 160 1.6

158 Z.B. Dong, Y.H. Wei / Theoretical and Applied Fracture Mechanics 46 (2006) 156–165



Fig. 2. 3D temperature distributions during multipass welding. (a) The first pass; (b) the second pass; (c) the third pass.




and the average maximum temperature rise valuecan be obtained.

3.2. Strain distributions and the driving force

during multipass welding

Fig. 5 presents the 3D transverse plastic straindistribution and the mechanical strain distributionin the weld centerline at 30 s during the first passwelding.

As shown in Fig. 5, the mechanical strain (thesum of the elastic and plastic strain) along the weldcentre line is compressive before the welding torch

approaches it. In the welding pool, the points

restore to its original strain free state at the instantof transforming from solid to liquid. Moreover, thetensile mechanical strain develops at the trailingedge of fusion weld pool due to the resolidified weldmetal. At the same time, this point situated in the

brittle temperature range, which the strength andductility of the metal are very low during solidifica-tion. Therefore solidification cracking occurs easilyin the brittle temperature range.

The driving forces are obtained according to sim-ulated thermal cycles (temperature against time)and mechanical strain cycles (mechanical strainagainst time). The evolution of the driving force toweld solidification cracks at different positions of the first pass weld is demonstrated in Fig. 6.

The mechanical strain curve for a particularpoint is plotted by monitoring both the temperaturedrop and the build-up of the mechanical strain asthat point is cooling down from the liquidus. Thecurve indicates how the driving force for solidifica-tion cracking varies during the solidification pro-cess. Fig. 6 suggests that the position at the end of the weld will experience the highest mechanicalstrain, and there is the smallest mechanical strainat the center of weld. The results predicate thatsolidification cracking is more likely to occur atthe start or end of the weld under the conditionsthat the plate is free of restraint, which agrees well

with the general concept.

Table 2The positions where temperature and strain were analyzed

Reference point a b c d e f

Coordinate (x, y, z) (50, 0, 3) (50, 4.05, 6.5) (50, 6, 10) (50, 7.7, 10) (50, 10, 10) (50, 15, 10)

0 100 200 300 400 500 600 700 8000

400

800

1200

1600

2000

2400

T e m p e r a t u r e ( º C )

Time (s)

Point aPoint bPoint c

0 100 200 300 400 500 600 700 8000

200

400

600

800

1000

1200

1400

A'

A


Time (s)

Point dPoint ePoint f

Fig. 3. Thermal cycle during multipass welding. (a) The thermalcycle of point a, b, c and (b) the thermal cycle of point d , e, f .

5 10 15 20 25 300

200

400

600

800

1000


Distance (mm)

Pass 3

Pass 2

Pass 1

Fig. 4. Average maximum temperature rise at different points onthe base plate.




Fig. 7 shows the 3D transverse plastic strain dis-

tribution and the mechanical strain distribution in

the weld centerline at 25 s during the second passwelding.

From the Fig. 7, it can be seen that transverseplastic strain distribution and the mechanical straindistribution patterns in the weld centerline duringthe second pass welding are similar to those of thefirst pass welding with different values only.

As shown in Fig. 8, the driving forces of the sec-ond pass weld at three different positions are smallerthan those of the first pass welding. It indicates thatthe weld solidification cracks are likely to occur dur-ing the first pass welding.

The mechanical strain and the driving force dis-tribution patterns of the third pass weld are alsosimilar to those of the first and second pass welds,the values of the third pass are smaller than theirs.

It is well known that the mechanical strain distri-butions of the first pass weld are affected by a sub-

sequent pass. Fig. 9 shows mechanical strains and

Fig. 5. Transverse strain distributions at 30 s during the first pass welding. (a) 3D transverse plastic strain distribution and (b) themechanical strain distribution in the weld centerline.

Fig. 6. Driving force curves for three locations on the first passweld centerline.




The schematic diagram of TVT apparatus is shownin Fig. 10.

As TVT is a pure bending process, the strain onthe top surface of the specimen is represented by theaverage strain calculated in Eq. (1)

eað%Þ ¼t

2

Rþ t

2

Â 100% %t

2 RÂ 100%; ð1Þ

where t is specimen thickness, R is radius of curva-

ture of the bending block.

However, the strain obtained by TVT is based onthe assumptions of pure bending and no localizeddeformation, and it neglects the strain concentra-

tion at the trailing edge of weld molten pool, asshown in Fig. 11.It can be seen that the strains at the trailing edge

of weld molten pool are the combined action of thebend strain of TVT and the local strain of weldingprocess, which decided the occurrence of weld solid-ification crack. Consequently, the applied averagestrains ea of TVT do not represent the true materialinherent resistance to cracking.

Therefore, this paper models the TVT to get thelocal strains in the vicinity of weld pool under differ-ent bending strains with FEM. The threshold strainsfor cracking initiation with modeling TVT replacethe applied average strains of TVT. Finally, thematerial resistance to weld solidification crack ismodified with modeling TVT. At the same time, to

R

F

Bending block

Fig. 10. Schematic sketch of Trans-Varestraint Test.

Fig. 11. Distribution of local strain.

Fig. 9. Mechanical strains distribution of first pass weld center-line. (a) Mechanical strain and temperature distributions duringsecond pass welding and (b) before and after second pass welding.

Fig. 12. Comparison of the local strains between TVT and MISO

measurements [17].




testify the computational local threshold strains inthe cracking susceptible temperature range, TVT issimulated at different bending strains. The localstrains are compared with the MISO [20] measure-ment of the local strain curve for solidification

cracks initiation as shown in Fig. 12 [17].It can be observed that the local strains obtainedwith modeling TVT coincide well with those mea-sured by MISO method.

4. Prediction of weld solidification cracks of walled

plates

The formation of weld metal solidification crack-ing results from the competition between the mate-rial resistance to cracking and the driving force to

cracking during the course of solidification of weldmetal, as shown in Fig. 13 [15]. Weld solidificationcracks occur only when the mechanical strainexceeds the threshold strain in the entire brittle tem-perature range.

Therefore, according to the relative position of the curves, the comparisons between the drivingforce of each pass and the material resistance canpredict the weld solidification cracks as shown inFig. 14.

Fig. 14 shows that the driving forces are smallerthan the material resistance of simulating TVT, so

there will not be solidification crack during multi-pass welding. The predicted result agrees well withthe experiments in the same welding conditionsand boundary conditions.

5. Conclusions

1. The multipass welding process of 10 mm SUS310stainless steel is modeled with finite elementmethod. The thermal cycle and strain cycle of each pass are simulated after taking into consid-eration of the fluid flow in the weld pool, thelatent heat, taking into account the effect of thedeformation in weld pool, change of initial tem-perature and solidification shrinkage.

2. The driving forces to weld solidification cracks of each weld pass are obtained successfully accord-ing to simulated results. It is found that the driv-ing force of first weld pass is larger than followingweld passes. Moreover, sequent welding processesaffect the mechanical strain distributions of previ-ous weld pass, of which the tensile mechanicalstrain changes to compressive strain.

3. Weld metal solidification cracks are predictedduring multipass welding according to the mate-rial resistance and the driving force. The pre-dicted results agree well with experiments.Therefore, the simulated results in this study pro-vide the foundation for predicting weld solidifica-tion cracking in actual weldment.

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ε

ΤTs

BTR

Material resistance

Tl

Liquid

Liquidus

Solidus Solid

Driving force

Fig. 13. Schematic explanations for occurrence of weld metal

solidification cracks [15].

Fig. 14. The prediction of weld metal solidification cracks of walled plates.




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Three Dimensional Modeling Weld Solidification Cracks

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