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Materials Science and Engineering A246 (1998) 4554

Numerical analysis of GTA welding process with emphasis onpost-solidification phase transformation effects on residual stresses1

B. Taljat *, B. Radhakrishnan, T. Zacharia

Oak Ridge National Laboratory, Metals and Ceramics Di6ision, Oak Ridge, TN 37831-6140, USA

Received 19 August 1997; received in revised form 3 October 1997

Abstract

The objective of this work was to analyze the residual stress state in spot welds made in an HY-100 steel disk by an autogenous

gas tungsten arc (GTA) welding process. An uncoupled thermal-mechanical finite element (FE) model was developed that took

into account the effects of liquid-to-solid and solid-state phase transformations. Effects of variations in mechanical properties due

to solid-state phase transformations on residual stresses in the weld were studied. Extensive experimental testing was carried out

to determine the mechanical properties of HY-100 steel. The residual stresses in the disk with the spot weld were measured by a

neutron diffraction (ND) technique. The FE results are in good agreement with the ND measurements. The results show that the

volumetric changes associated with the austenite to martensite phase transformation in HY-100 steel significantly affect residual

stresses in the weld fusion zone and the heat affected zone. 1998 Elsevier Science S.A. All rights reserved.

Keywords: Finite element method; Gas tungsten arc; Residual stress state; Neutron diffraction

1. Introduction

One of the major problems in welded structures is

residual stress and distortion. Residual stresses that

develop in and around the welded joint are detrimental

to the integrity and the service behavior of the welded

part. High residual tensile stresses in the region near the

weld might promote brittle fracture, reduce the fatigue

life, and promote stress corrosion cracking during ser-

vice. Residual tensile stresses also promote cold crack-

ing in association with hydrogen in certain steels, even

before the welded member is put in service.

Because a weldment is heated locally by the welding

heat source, temperatures in the vicinity of the weld-

ment are not uniform but change with distance from

the weld centerline. Due to localized heating, complex

thermal stresses are generated during welding. Residual

stresses are stresses that remain in a material as a result

of liquid-to-solid phase transformation associated with

weld solidification and the subsequent non-uniform

cooling of the weld altered by phase transformations in

the solid state.

Several factors may contribute to the formation of

residual stresses [1 7]. The plastic deformation pro-

duced in the base metal (BM) is a function of struc-

tural, material, and fabrication parameters. The

structural parameters include the geometry, thickness,

and joint design. The material parameters reflect the

metallurgical condition of the base material and the

weld metal. Fabrication parameters include the welding

process, procedure, parameters, and the degree of

restraint.

In steel weldments, the solid-state transformation on

cooling of austenite to martensite has a major influence

on the residual stresses. The volumetric expansion at a

given location in the heat-affected zone (HAZ) or the

fusion zone (FZ) depends upon the volume fraction of

martensite that forms. The extent of martensitic trans-

formation depends upon the kinetics of other diffu-

* Corresponding author. Tel.: +1 423 5744837; fax: +1 423

5744839; e-mail: [email protected] The submitted manuscript has been authored by a contractor of

the US Government under contract No. DE-AC05-96OR22464. Ac-

cordingly, the US Government retains a nonexclusive, royalty-free

license to publish or reproduce the published form of this contribu-

tion, or allow others to do so, for US Government purposes.

0921-5093/98/$19.00 1998 Elsevier Science S.A. All rights reserved.

PII S 0 9 2 1 - 50 9 3 9 7 0 0 7 2 9 - 6

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B. Taljat et al. /Materials Science and Engineering A246 (1998) 455446

Table 1

Chemical composition of HY-100 material (wt.%)

NiC Cr Mn Si Mo Cu P S Al

1.4 0.280.18 0.262.8 0.18 0.17 0.044 0.029 0.013

sional transformations. The diffusional transformationkinetics are complicated because the austenite composi-

tion in the HAZ is not homogeneous. This is due to the

rapid heating and cooling associated with the welding,

and insufficient time available for austenite homoge-

nization especially at those locations where the on-heat-

ing peak temperatures are just above the trans-

formation temperature. It is known that inhomoge-

neous austenite transforms more readily to diffusional

products because of the ease of nucleation of the equi-

librium phases. The diffusional transformation kinetics

also depend upon the austenite grain size, since austen-

ite grain boundaries are preferred nucleation sites forthe austeniteferrite transformation. The grain size

dependence becomes more complicated in the weld

HAZ because of the variation of grain size with posi-

tion in the HAZ. Solidification may introduce composi-

tion fluctuations in the FZ with respect to

substitutional elements. It is known that substitutional

elements play a major role in the kinetics of diffusional

transformations [8].

The objective of this study was to analyze the resid-

ual stress state in spot welds made in HY-100 steel by

an autogenous gas tungsten arc (GTA) welding process.

A finite element (FE) model for residual stress analysisin spot welds was developed. The analysis included

both the mechanical property changes and the volumet-

ric changes due to the austenitemartensite transfor-

mation. Effects of variation in mechanical properties at

high temperatures and the variation due to transforma-

tion of austenite to martensite on residual stresses were

evaluated. The results were compared with experimen-

tal measurements of residual stresses [9 11] in the

HY-100 steel weldment using the neutron diffraction

(ND) technique.

2. Experimental

The chemical composition of HY-100 steel is shown

in Table 1. The carbon equivalent (CE) of the steel

calculated using the formula: CE=C+Mn/6+(Cr+

Mo+V)/5+(Ni+Cu)/15 is 0.74 wt%. The engineering

stressstrain curves were determined by a conventional

tensile test for the temperature range between 293 and

1273 K (Fig. 1). To obtain true stress strain curves,

which are the required input to the FE code, a linear

work hardening was assumed with the rate of 500 MPa.

Thermal expansion of the material was determined inthe range between room temperature and the solidus

temperature. A high speed quenching dilatometer was

used to carry out these measurements. The mean coeffi-

cient of thermal expansion (CTE) was calculated from

the dilatometer data using the solidus temperature as a

reference (Fig. 2). The solidus and the liquidus temper-

atures for the HY-100 steel composition determined

using Thermocalc are 1741 and 1776 K, respectively.

Other properties, such as elastic modulus, Poissons

ratio, thermal conductivity, density, and latent heat

were found elsewhere [12,13].

An autogenous GTA welding process was used tomake a spot weld at the center of a HY-100 steel disk

(19 mm in height and 75 mm in diameter) with a

welding current of 320 A and a voltage of 15 V, using

4 mm diameter electrode. Welding arc time was 5 s with

argon shielding, followed by a 5 s postweld purge with

argon gas. During welding, the disk was set on a table

and no additional restraints were applied. Fig. 3 shows

the welding set-up.

The disk was sectioned along the z axis through the

center of the weld. One half was used for the ND

residual stress measurements and the other half was

used for microhardness measurements and metallogra-

phy. Redistribution of residual stresses due to section-

ing of the disk was not taken into account.

Fig. 1. Engineering tensile stressstrain curves for HY-100 measured

at various temperatures.

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B. Taljat et al. /Materials Science and Engineering A246 (1998) 4554 47

Fig. 2. Thermal expansion and coefficient of thermal expansion for

HY-100. Note the length of cylindrical specimens used to measure

CTE is 8 mm.

3. Fe modeling

Complex numerical approaches are required to accu-

rately model the welding process. In thermal analysis,

one should account for: (1) conductive and convective

heat transfer in the weld pool; (2) convective, radiative,

and evaporative heat losses at the weld pool surface; (3)

heat conduction into the surrounding solid material, aswell as the conductive and convective heat transfer to

ambient temperature. Furthermore, one needs to ac-

count for temperature dependent material properties

and the effects of liquid-to-solid and solid-state phase

transformations in the material. Capturing all of the

above effects results in a model that cannot always be

realistically solved. However, some of these effects may

not significantly influence the residual stress calcula-

tions, and yet they considerably complicate the analysis.

Therefore, simplifying assumptions should be used judi-

ciously for establishing a reasonably effective and accu-

rate FE model.

The residual stress distribution was computed usingan uncoupled thermo-mechanical FE formulation using

ABAQUS FE code [15]. The computations used temper-

ature-dependent thermo-physical and mechanical prop-

erties of the BM. The thermal analysis was based on the

heat conduction formulation with the Gaussian heat

input from the arc.

An axisymmetric FE model was developed using

linear four-noded finite elements, as shown in Fig. 7.

The core of the modeling effort was the development of

user subroutines to the ABAQUS code, which were used

to model the welding arc in the thermal analysis and to

incorporate the phase transformation effects in themechanical analysis. Thermal and mechanical analysis

were uncoupled and conducted sequentially. First, the

thermal analysis was carried out calculating the tran-

sient temperature distributions during welding. The me-

chanical part relied on the thermal analysis results and

calculated the stressstrain distribution on the basis of

the temperature history. The mechanical model was

similar to the thermal model, except for the type of finite

elements and the applied boundary conditions.

To justify the expensive and time-consuming experi-

mental work for determining the high temperature me-

chanical properties of regions that undergo theon-heating and on-cooling phase transformations, as

well as of regions that do not experience these transfor-

mations, a sensitivity analysis was carried out to deter-

mine the temperature and microstructure dependence of

yield strength on residual stresses in the weld.

3.1. Thermal analysis

The welding arc was modeled by introducing a heat

flux to the disk surface. To account for heat transfer

effects due to fluid flow in the weld pool, an increase in

Metallographic observations together with the

dilatometer measurements indicate a martensite mi-

crostructure in the HAZ and FZ, with extensive crack-

ing in the FZ. Fig. 4(a) and (b) show the r z and r

section of the weld structure, respectively.

Microhardness was measured in order to determine

the yield strength in the HAZ and the FZ. According to

Cahoon [14], the correlation between yield strength, |y,

and the Vickers hardness, Hv, can be expressed as:

|y(my=me+0.002)=Hv

3

my0.08

n$

Hv

30.1n (1)

where n is the strain hardening coefficient, me is the

elastic strain at yield stress (me=sy/E), and E is the

Youngs modulus.

Fig. 5 shows the measured Vickers hardness across

the FZ, HAZ and BM. Hardness of the FZ and HAZ

(425475 Hv) is considerably higher than that of the

BM (about 280 Hv). The hardness in the center of the

FZ is about 425 Hv and linearly increases to about 475

Hv in the HAZ. The strain hardening coefficient for the

BM was determined by Eq. (1), using the yield strength

obtained in tensile tests and the measured hardness of

the BM. The strain hardening coefficients of the HAZ

and FZ were assumed to be equal to that of the BM.

According to Eq. (1), the yield strength of the HAZ and

FZ that corresponds to a hardness of 425475 Hv is

12141357 MPa.

The ND measurements were carried out on the

BEAM Tube-6 (BT-6) triple-axis spectrometer at the

National Institute of Standard and Technology research

reactor [10,11]. The measurements were made using a

nominal gauge volume of 333 mm. Fig. 6 shows

the positions and relative sizes of the measurement

points which are located on the radial section plane.

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Fig. 3. Welding setup (dimensions are in mm).

thermal conductivity above the melting temperature

was assumed. The thermal effects due to solidification

of the weld pool were modeled by taking into account

the latent heat of fusion. To account for heat losses,

both the radiative and convective heat transfer at the

weld surface were modeled.

The overall heat flux was calculated as:

F=pEI (2)

where p represents the efficiency factor, which accounts

for radiative and other losses from the arc to the

ambient environment, E is voltage, and I electric cur-

rent. Heat flux distribution at the disk surface was

defined by the equation:

f(r)=f1e3(r/r0)

2

(3)

where r is the radial coordinate with the origin at the

spot weld center. The constant r0 represents the charac-

teristic arc dimension in the r direction within which

95% of the energy is transferred. The constant f1 can be

derived by integrating the function f(r) at the material

surface:

f1=pEI 3yr20

(4)

To account for heat transfer due to fluid flow in the

weld pool, the thermal conductivity was assumed to

increase linearly between the solidus temperature and

3000 K by a factor of three [4] (Z. Feng, Edison

Welding Institute, 1997, personal communication). Fig.

8 shows the specific heat and thermal conductivity used

in the analysis.

The latent heat of fusion was specified to model the

heat released during solidification. The value of 247 J

g1 was used [13]. The tube-air convection coefficient

was calculated for the natural convection to the air at

293 K. Radiative heat transfer was assumed at the top

disk surface with an emissivity coefficient e=0.2 [16].

Two computational steps were carried out to com-

plete the thermal welding simulation. In the first step,

the heating/melting of the material was modeled by

applying the heat flux. Cooling transients were calcu-

lated in the second step, when the heat source was

removed and the disk was cooled to room temperature.

The heating time was 5 s, whereas the disk was cooled

until the ambient temperature was reached.

3.2. Mechanical analysis

Rate-independent elastic-plastic constitutive equa-

tions were constructed from the uniaxial tensile test

results of the BM at various temperatures. A linear

transition between the yield strength of the BM at 573

K, the beginning of the martensite transformation, and

the yield strength of martensite at room temperature, as

calculated from the hardness data, was assumed. Both

yield and ultimate strengths were reduced to 5.0 MPa at

the melting temperature to simulate low strength at

high temperatures. Elastic modulus and Poissons ratio

were also given as functions of temperature. The elastic

modulus was reduced to a small value (5.0 GPa) at high

temperatures.

The same FE mesh as in the thermal analysis was

used here, except for the element type and different

boundary conditions. The analysis is based on the

temperature history calculated in the thermal analysis

which represents the input information. The movement

in the axial direction of the bottom disk surface was

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Fig. 4. Weld structure: (a) rz section; (b) r section.

restrained to appropriately model the actual welding

conditions.

A subroutine to ABAQUS code was developed that

accounts for changes in mechanical properties and vol-

umetric changes due to the phase transformation. The

program consists of two parts:

The thermo-physical and mechanical properties of

the BM were used for the entire model during heating.

The temperature history of each integration point in the

model was observed during cooling. Depending on the

peak temperature that a particular point reached during

the heating transient, and depending on the cooling

time, the decision was made whether the point under-

went the martensitic transformation or not. For each

point that underwent the transformation the material

properties of the martensitic phase were applied.

The subroutine also provided the basis for calculat-

ing the volume increase due to martensitic phase devel-

opment. At this stage, the volume change was

approximated by the introduction of a modified coeffi-

cient of thermal expansion. The program distinguished

between the heating and cooling cycle of each point and

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Fig. 5. Vickers hardness of weld and base material.

Fig. 7. FE model (dimensions are in mm).

in Fig. 9, Case 1 considers all effects, which means

higher yield strength at lower temperatures for the

material that undergoes the phase transformation, the

experimentally determined mechanical properties athigh temperatures, and the assumption of lower yield

strength at temperatures close to the melting point.

Case 2 is the same as Case 1, except it does not consider

the change in the yield strength due to the phase

transformation. Case 3 assumes a linear decrease in

yield strength from room temperature to the melting

temperature.

4. Results and discussion

Fig. 10 shows the radial, axial, and tangential resid-ual stresses at the weld centerline and at a radius of 10

mm. The radial stresses in the FZ and HAZ at R=0

are as high as 580 MPa. Stresses in the BM adjacent to

HAZ increase to almost twice that value and then

the appropriate CTE curve was used (Fig. 2). Note thatthe part of the CTE curve that represents the austen-

itemartensite phase transformation was only used on

the cooling cycle for the points that satisfied the trans-

formation criteria explained above. The CTE values

were calculated with respect to the reference tempera-

ture of 1741 K (solidus temperature). Note that in this

case the CTE defines contraction of the material at

temperatures below the reference temperature. The

CTE value above the melting point was set to zero in

order to disable the calculation of thermal stresses in

the weld pool, whose values might otherwise be signifi-

cant due to high temperatures.Three different cases were studied to analyze the

effect of yield strength at high temperatures and the

effect of yield strength after the austenitemartensite

phase transformation on the residual stresses. As shown

Fig. 6. HY-100 disk with ND measurement locations.

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Fig. 8. Specific heat and thermal conductivity for HY-100.

Fig. 10. Comparison of FE and ND results in radial, axial, and

tangential direction at R=0 mm and R=10 mm.

gradually decrease to compressive stress in the far BM.

Lower stresses in the FZ and HAZ can be explained by

the volume change of the material that undergoes the

austenitemartensite phase transformation. The tem-

peratures in the BM adjacent to the HAZ do not reach

the transformation temperature, therefore, no phase

transformation occurs there, which means no volume

change to offset high stresses. The tangential stress

distribution at R=0 is very similar. The axial stresses

are lower and reach the magnitude of 240 MPa. Calcu-

lated radial and tangential residual stresses agree well

with the ND measurement, whereas the calculated axial

stresses are lower than measured by about 200 MPa. In

comparing the results, one should remember that each

ND data point represents an average residual stress

over a 333 mm volume. The radial residual

stresses at R=10 mm are tensile and lower. The agree-

Fig. 9. Yield stress for the assumed cases.

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ment with the ND results is very good. The magnitude

of axial stresses is very small, which is also shown by

the ND results. The tangential stresses are compressive

and of a low magnitude. They are not in agreement

with the first ND data point, but agree with the rest of

the ND results. Fig. 11 shows the radial, axial, and

tangential stress distribution in the weld region.

The results presented in Figs. 10 and 11 take intoaccount the phase transformation effects. Another anal-

Fig. 12. Residual stress comparison with the case of no phase

transformation effect at R=0 and R=10 mm.

Fig. 11. Residual stress distribution; radial, axial, and tangential

component (deformation is magnified 5). Note the different stress

scale for axial stresses.

ysis was carried out without considering these effects,

and the comparison is shown in Fig. 12. The results

show a significant effect of phase transformation on

residual stresses. This can be explained by the mi-

crostructural changes that occur during the austenite

martensite phase transformation in the FZ and HAZ

that affect both the yield strength and CTE, which, in

turn, have a significant effect on the residual stress. The

increased yield strength in the FZ and HAZ, as indi-

cated by the changes in hardness (Fig. 5), allows higher

residual stresses. On the other hand, the higher hard-

ness in the FZ and HAZ is related to the formation of

martensite in these locations, which is accompanied by

a volume expansion that reduces the thermal contrac-

tion. This effect tends to reduce the residual stress level

in the FZ and HAZ.

Several computations evaluating the influence of

variations in mechanical properties at high tempera-

tures, and the effect of higher yield strength due to

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martensite formation during cooling, were carried out.

Three cases were analyzed, as described previously, and

the comparisons are shown in Fig. 13. The results show

that the effect of higher yield strength due to formationof martensite does not affect the residual stresses in the

weld. The assumption of linear decrease in yield

strength with temperature has a notable effect on theresidual stresses, which suggests that accurate tempera-

ture dependent mechanical properties are required.

One can conclude that in such analysis it is not asimportant to account for changes in the stressstrain

data due to the austenitemartensite phase transfor-mation, as it is to account for the volumetric changes in

the material caused by the phase transformation, and to

provide accurate, temperature-dependent stress straindata for the austenitic and ferritic phases.

There are several possibilities for improving the

present model. The thermal analysis is based on theconduction model and the assumption of a Gaussian

shape for the heat source. The accuracy of calculated

residual stresses depend on the calculated temperaturetransients; therefore, future efforts will concentrate on

implementation of the arc-pool interaction effect (the

effects of arc-to-weld pool evolution and free weldsurface deformation) into the current thermal model. A

convective heat transfer model, which includes the fluidflow effects in the FZ, is also being developed. These

changes would improve the calculated temperature

transients which have an effect on the calculated resid-ual stresses.

The current model relies upon experimentally deter-

mined transformation kinetics to incorporate the trans-formation plasticity effects. However, it is of

fundamental interest to develop modeling capabilities

that will predict the austenite transformation kineticsunder non-equilibrium welding conditions. As a first

step, it is necessary to model the HAZ grain structurefor a given weld thermal cycle. Previous studies [17]

using 2D Monte Carlo simulations captured the effect

of thermal pinning in the HAZ of a 1/2Cr-Mo-V steel.The simulations are now being extended to two-phase

microstructures where the second phase is an insoluble

inclusion. Both 2 and 3D Monte Carlo simulationshave been carried out in the past to predict the influ-

ence of inclusion volume fraction, size, shape, etc. on

the pinned grain size (unpublished research). The re-sults indicate that there is a significant difference in the

nature of grain boundary pinning by inclusions between

2 and 3D. Hence, in order to make a realistic predictionof grain size in the HAZ of materials containing second

phase particles, one has to resort to a 3D simulationthan a 2D simulation.

5. Conclusions

An FE model for residual stress analysis in spotwelds, which accounts for the phase transformation

effects, was developed. The computations were carried

out using ABAQUS code.Fig. 13. Residual stress comparisons of the three analyzed cases. Note

the results of Case 1 and 2 overlay.

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An experimental program was carried out to deter-

mine material properties of HY-100 steel. These include

tensile testing, measurement of the CCT curve, metallo-

graphic observations, and hardness measurements. The

hardness measurements show increase in hardness in

the HAZ and the FZ, which indicate the phase trans-

formation from austenite to martensite. The hardness

values were used to determine the yield strength in theHAZ and the FZ. The metallographic observations

show the martensitic structure in the FZ.

The ND technique was used to measure residual

stresses in the spot weld. The FE results are generally in

good agreement with the ND results. The results show

a considerable effect of phase transformation on resid-

ual stresses, which cannot be neglected in such analysis.

The volume change during the austenitemartensite

phase transformation tends to relieve high tensile

stresses, and this is the reason that the magnitude of

radial and tangential stresses in the HAZ and FZ is

about one-half the stress magnitude in the BM adjacent

to the HAZ. The results also show that the effect of

volume change on residual stresses is more significant

than the effect of higher yield strength caused by the

phase transformation. The results also indicate the sig-

nificance of temperature dependent stress strain data

for accurate prediction of residual stresses.

Acknowledgements

The authors would like to thank Dr C.R. Hubbard

and Dr X.L. Wang for reviewing the paper. The re-

search was sponsored in part by an appointment to theOak Ridge National Laboratory Postdoctoral Research

Associates Program administered jointly by the Oak

Ridge Institute for Science and Education and Oak

Ridge National Laboratory. The research was also

sponsored by the US Navy, Office of Naval Research,

under interagency agreement DOE No. 1866-E126-A1,

Navy No. N000014-92-F-0063 under US Department

of Energy contract DE-AC05-96OR22464 with Lock-

heed Martin Energy Research Corporation.

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