1.c heat flow and temperature distribution in welding.pdf

7/21/2019 1.c Heat Flow and Temperature Distribution in Welding.pdf

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Equation (1-103) has been plotted in Fig. 1.36.

(1-103)

Example

(LU)

Consider butt welding ofa2mm thin plate of austenitic stainless steel with covered electrodes

(SMAW) under the following conditions:

Calculate the retention time within the critical temperature range for chromium carbide

precipitation (i.e. from 650 to 850

0

C) for points located at the 850

0

C isotherm.

Solution

If

we

use the melting point of

the

steel as

a

reference tem perature, the parameter n

3

/5 becomes:

A comparison with Fig. 1.35 shows that the assumption of 1-D heat flow is justified when

Q

p

99% Al)

under the following conditions:

Based on Fig. 1.43, sketch the peak temperature contours in the transverse section of the

weld at pseudo-steady state.


11/45

Solution

If we neglect the latent heat of melting, the parameter

n

3

at the chosen reference temperature

(T

c

=

T

m

)

becomes:

Similarly, when

v

= 3mm s

l

and

a =

85mm

2

s

1

we obtain the following value for the di-

mensionless plate thickness:

Readings from Fig. 1.43 give:

e

p

^ ,

(

0

C) Model System Com ments

0.50

1.0 34 0660

M edium thick Heat flow

inxa ndy

directions,

plate solutio n partial heat flow

in

z

direction

0.17 ->

0.50 130 -> 340

Thin plate solution Heat flow

in

x

and

ydirections,

(2-D heat flow) negligible heat flow

in

z direction

we obtain:

(1-107)


22/45

where

and

Note that equation (1-107) correctly reduces to equation (1-106) when

A

approaches zero.

The total temperature rise in point

P

is then obtained by superposition of the temperature

fields from the different elementary heat sources, i.e.:

(1-108)

where

In practice, we can subdivide the heat distributions into a relatively small number of el-

ementary point sources, and usually a total number of 8 to 10 sources is sufficient to obtain

good results (i.e. smooth curves). How ever, the relative strength of each heat source and their

distribution along the y- and z-axes must be determined individually by trial and error by

comparing the calculated shape of the fusion boundary with the real (measured) one.

Figure 1.55 show s the results from such calcu lations, carried out for a single pass (bead-in-

groove) GM A steel weld. It is eviden t that the important effect of the weld crater/weld finger

formation on the HA Z peak temperature distribution is adequately accoun ted for by the present

model. A weakness of the model is, of course, that the shape and location ofthefusion bound -

ary must be determined experimentally before a prediction can be made.

1.10.5.2 Simplified solution

Similar to the situation described above, the point heat source will clearly not be a good

model w hen the heat is supplied over a large

area.

Welding with a weaving techn ique and sur-

facing with strip electrodes are prime examples of this kind.

Model (after G rong and Christensen

19

)

As a first simplification, the Rosen thal thick plate solution is considered for the limiting case

of a high arc power

q

o

and a high welding speed D, maintaining the ratio

q

o

Iv

within a range

applicable to arc welding. Consider next a distributed heat source of net pow er density

q

o

I2L

extending from

-L

to

+L

on either side of the weld centre-line in the y-direction*, as shown

schem atically in Fig . 1.56. It follows from eq uation (1-73) that an infinitesimal source dqy

located between

y

and

y

+

dy

will cause a small rise of temperature in point

P

at time f, as:

(1-109)

Alternatively, we can use a Gaussian heat distribution, as shown in App endix 1.4.

where

and


23/45

z

m

m

)

Shaded region indicates

fusion zone

y (mm)

Fig.1.55.

Calculated peak tem perature con tours in the transverse section ofaGMA steel weldment (Op-

erational conditions: / = 450A,

U -

30V,

v=

2.6mm s

1

,

d=

50mm).

2-D heat flow

Fig.

1.56.

Distributed heat sou rce of net power density qJ2L on a semi-infinite body (2-D heat flow).


24/45

(1-110)

where

erf(u)

is the Gaussian error function (previously defined in Appendix 1.3).

Peak temperature distribution

Because of the complex nature of equation (1-110), the variation of peak temperature with

distance in the

y-z

plane can only be obtained by numerical or graphical methods. Accord-

ingly, it is convenient to present the different solutions in a dimensionless form. The following

parameters are defined for this purpose:

Dimensionless operating parameter:

Dimensionless time:

Dimensionless y-coordinate:

Dimensionless z-coordinate:

(1-111)

(1-112)

(1-113)

(1-114)

(1-115)

By substituting these parameters into equation (1-110), we obtain:

where 0 is the dimensionless temperature (previously defined in equation (1-9)).


25/45

The variation of peak temperature

Q

p

with distance in the

y-z

plane has been numerically

evaluated from equation (1-115) for chosen values of P and 7 (i.e. P = 0,

3

= 3 /4, P = I , and

7 = 0). The results are presented graphically in Figs. 1.57 and 1.58 for the through thickness

(z

=

z

m

)

and the transverse

(y

=

y

m

)

directions, respectively. These figures provide a systematic

basis for calculating the shape of the weld pool and neighbouring isotherms under various

welding co nditions.

In Fig. 1.59 the weld width to depth ratio has been computed and plotted for different

combinations of

n

w

and 9

p

. It is evident that the predicted w idth of the isotherms generally is

much greater, and the depth correspondingly smaller than that inferred from the point source

mode l. Such deviations tend to becom e less pronounced with decreasing peak temperatures

(i.e.

increasing distance from the heat sou rce). At very large value ofn

w

,the theoretical shape

oftheisotherms approaches that ofasemi-circle, which is characteristic ofapoint heat source.

Example (1.13)

Consider GMA welding with a weaving technique on a thick plate of low alloy steel under the

following conditions:

Sketch the contours of the fusion boundary and the Ac

r

isotherm (71O

0

C) in the

y-z

plane.

Compare the shape of these isotherms with that obtained from the point heat source model.

Solution

If we neglect the latent heat of melting, the operating parameter at the chosen reference tem-

perature

(T

c

=

T

m

)

becomes:

Fusion boundary

Here we have:

Readings from Figs. 1.57 and 1.58 give:

Ac j-temperature

In this case the peak temperature should be referred to 720

0

C, i.e.:


26/45

e

n

w

e

n

w

V -

Fig. / .57 .

Calculated pea k temp erature distribution in the through-thickness direction of the plate at dif-

ferent positions along the weld surface.

y

m

/L

Fig.1.58.

Calculated p eak tem perature distribution in the transverse direction of the plate at position

y

Z) = 0.


27/45

y

m

z

m

Fig.1.59.Effects ofn

w

and d

p

on the weld w idth to depth ratio.

n

w

from which

Readings from Figs. 1.57 and 1.58 give:

Similarly, equation (1-75) provides a basis for calculating the width of the isotherms in the

limiting case where all heat is concentrated in a zero-vo lume point. By rearranging this equa-

tion, we obtain:

which gives

6.3 mm when

B

p

=

1(T

p

=

1520

0

C)


28/45

and

Figure 1.60 shows a graphical presentation of the calculated peak temperature contours.

Implications of model

It is evident from Fig. 1.60 that the pred icted shape of the isotherm s, as evaluated from equ a-

tion (1-110), departs quite strongly from the semi-circular contours required by a point heat

source. Mo reover, a closer inspection of the figure shows that inclusion of the he at distribution

also gives rise to systematic variations in the weld thermal programme along a specific

isotherm, as evidenced by the steeper tem pera ture gradient in the v-direction com pared with

the z-direction of theplate.This point is more clearly illustrated in Fig. 1.61, which com pares

the HAZ temperature-time programme for the two extreme cases of

z =

0 and y = 0, re-

spectively. It is obvious from Fig. 1.61 that the retention time within the austenite regime is

considerably longer in the latter case, although the cooling time from 800 to 500

0

C,

Af

8/5

,

is

reasonab ly similar. These results clearly underline the imp ortan t difference betw een a point

heat source and a distributed heat source as far as the weld thermal program me is concerned .

Model limitations

In the present model, we have used the simplified solution for a fast moving high power

source (equation

1-73))

as a starting point for predicting the te m pera ture- time patte rn. Since

the equations derived later a re ob tained by integrating equation (1-73), they will, of course,

apply only under conditions for which this solution is valid.

Moreover, a salient assumption in the model is that the heat distribution during weaving

can be represented by a linear hea t source orientated perpendicular to the welding direction.

Although this is a rather crude approximation, experience shows that the assumed heat dis-

when

z,

mm

Fig. / .60 .Predicted shape of fusion boundary and Ac pisoth erm during GM A welding of steel with an

oscillating electrode (Example1.13). Solid

lines:

D istributed heat source; Broken

lines:

Point heat source.


29/45

T

m

a

u

e

0

C

Time,s

Fig.

L61.

Calculated HAZ thermal cycles in positions

y

=

0

and

z

=0 (Example1.13).

tribution is not critical unless the rate of weaving is kept close to the travel speed. However,

for most practical applications weaving at such low rates would be undesirable owing to an

unfavourable bead morphology.

Case Study (1.2)

Surfacing with strip electrodes m akes a good case for application of equation (1-110). Specifi-

cally, we shall consider SA welding of low alloy steel with 60mm X 0.5mm stainless steel

electrodes. The operational conditions employed are listed in Table 1.5.

It is evident from the metallograph ic data presented in Fig. 1.62 that neither the bead pen-

etration nor the HA Z depth (referred to the plate surface) can be pred icted readily on the basis

of the present heat flow model when welding is carried out with a consumable electrode,

owing to the formation ofareinforcement. Th is situation arises from the simplifications made

in deriving equation (1-110). The problem , however, may be eliminated by calculating the

depth ofthe

Ac

3

and

Ac

1

regions relative to the fusion boundary, i.e. Az

m

=

z

m

(Q

p

) - z

m

(Q

p

= 1),

orAy

m

=

y

m

(8

p

) - y

m

(6

p

= 1), for specific p ositions along the w eld fusion line, as shown by the

solid curves in Fig. 1.62 for

Q

p

= 0.54 and 0.45, respectively. An inspection of the graphs

reveals satisfactory agreement between theory and experiments in all three cases, which im-

plies that the model is quite adequate for predicting the HA Z thermal program me as far as strip

electrode welding is concerned. This result is to be expected, since the assump tion of two-

dimensional heat flow is a realistic one under the prevailing circumstances.

Case Study (1.3)

As a second exam ple we shall consider GTA welding (without filler wire additions) at various

heat inputs and amplitudes of weaving w ithin the range from

1

to 2.5 kJ mm

1

and 0 to 15mm,

respectively. Data for welding parameters are given in Table 1.6.


30/45

y, mm

Fusion line

y, mm

Weld S4

Stainless steel

z,

mm

Weld

S3

Stainless

steel

z,

mm

y, mm

Stainlesssteel

z,mm

Weld S5

Fig.1.62.Com parison between o bserved and predicted

Ac

3

and

Ac

1

contours during strip electrode w eld-

ing (Case study

1.2).

Data from Grong and Christensen.

19

ble

1.5Operational conditions used

in

strip electrode w elding experimen ts (Case study

1.2).

Base metal/ Weld

/ U v 2L n

w

filler metal No. A) V) (mms

1

) mm) Cn= 0.7)

combination

S3 730 27 1.8 60 0.34

Low alloy steel/

stainless steel

S 4 7 3

2 7 2

-

2

60 0.28

S5

730 27 2.5 60 0.24


31/45

ble

1 6

Operational conditions used in GTA welding exp eriments (Case study 1.3).

I U v 2L n

w

WeIdN o. (A) (V) (mm s

1

) (mm) V= O-

1 2

T]= 0.23

B l 200 13.5 2.6 9.5 0.20 0.40

B2 200 14.0 1.1 15.0 0.20 0.40

B3 200 13.5 2.5 -

B4 200 12.5 1.0

Calibration procedure

In genera l, a com parison betw een theory and experiments requires that the arc efficiency fac-

tor can be established with a reason able degree of accuracy. Unfortunately, the arc efficiency

factor for GTA welding has not yet been firmly settled, where values from 0.25 up to 0.75 have

been reported in the literature (see Table 1.3). Add itional prob lems resu lt from the fact that

only a certain fraction of the total amount of heat transferred from the arc to the base plate is

sufficiently intense to cause m elting. This has led to the introduction of the melting efficiency

factor T]

m

, which normally is found to be 30-70% lower than the total arc efficiency of the

process, depending on the latent heat of melting, the applied amperage, voltage, shielding gas

comp osition, or electrode vertex angle.

23

Consequently, since these parameters cannot readily

be obtained from the literature, the following reasonable values for

r\

m

and

r\

have been as-

sumed to calculate

n

w

in Table 1.6, based on a pre-evaluation of the experimental data:

j

m

=

0.12 (fusion zone),TI= 0.23 (HAZ ).

It should be noted that the above va lues also include a correction for three-dimensional heat

flow, since the assumption of a fast moving high power source during low heat input GTA

welding is not valid. Hence, both the arc efficiency factor and the melting efficiency factor

used in the present case study are seen to be lower than those commonly employed in the

literature.

Full weaving (welds Bl and B2)

The results from the metallographic examination of the two GTA welds deposited under full

weaving conditions are presented g raphically in Fig. 1.63. Note that the shape of the fusion

boundary as well as the

Ac

3

and the

Ac

1

isotherms can be predicted adequately from the present

model for both combinations of

E

and

L

(an exception is the HAZ end points in position

z

= 0),

provided that proper adjustments of

i\

m

and

Tj

are made . The good correlation obtained in Fig.

1.63 between the observed and the calculated peak temperature contours justifies the adapta-

tion of the model to low heat input processes such as GTA welding, despite the fact that the

assumption of two-dimensional heat flow is not valid under the prevailing circumstances.

No weaving (welds B3 and B4)

For the limiting case of no weaving (Fig.

1.64),

the concept of an equivalent amplitude of

weaving has been used in order to calculate the peak temperature contours from the model.

This parameter (designated

L

eq

) takes into account the effects of convectional heat flow in the

weld pool on the resulting bead geometry, and is evaluated empirically from measurements of

the actual weld samples. At low heat inputs (Fig.1.64 a)),the agreement between theory and


32/45

Weld B1

z, mm

y, mm

Fusion line

y,

mm

Weld B2

z, mm

Fig. 1.63.Comparison between observed and predicted fusion line,

Ac

3

andAc

1

contours during GTA

welding under full weaving conditions (Case study 1.3). Data from Grong and Christensen.

19

experiments is largely improved by inserting2L

eq

=

7.5mm into equation (1-110), when com -

parison is made on the basis of the point source mo del. In contrast, at a heat input of 2.5 kJ

mm

1

(Fig.1.64 b)),the measured shape of the H AZ isotherms is seen to approach that of a

semi-circle, and hence the deviation between the present model and the simplified solution for

a fast moving high power point source is less apparent.

Intermediate weaving

At intermediate am plitudes of weaving (2L = 5 and 7.5mm, respec tively), convectional heat

flow in the weld pool will also tend to increase the bead width to depth ratio beyond the

theoretical value predicted from the presen t model, as shown in

Fig.

1.65. The plot in

Fig.

1.65


33/45

Weld B3

y, mm

z, mm

Fusion line

y, mm

eld B4

z, mm

Fig.

1.64.

Comparison between observed and predicted fusion line,Ac

3

andAc

1

contours during GTA

welding with a stationary arc (Case study 1.3). Solid

lines:

Distributed heat source, Broken

lines:

Point

heat source. Data from Grong and Christensen.

19

includes all data obtained in the GTA welding experiments with an oscillating arc, as reported

by Grong and Christensen.

19

These results suggest that the applied amplitude of weaving must

be quite large before such effects become negligible. Consequently, adaptation of the model to

the weld series considered above would require an empirical calibration of the weaving am pli-

tude similar to that performed in Fig. 1.64 for stringer bead weldments to ensure satisfactory

agreement between theory and experiments.

1.10.6

Thermal conditions during interrupted welding

Rapid variations of temperatures as a result of interruption of the welding operation can have

an adversely effect on the microstructure and consequently the mechanical properties of the

weldment.


34/45

W

i

d

h

o

d

e

h

r

a

o

Theoretical

curve

Depth

Width

Fig. 1.65.Comparison between observed and predicted weld width todepth ratios during GTA welding

withanoscillating arc (Case study 1.3). D ata from Grong and Christensen.

19

n

w

t,t

T,e

Fig.1.66.Idealised heat flow modelforpredictionoftransient temperatures during interrupted welding.


35/45

Model (after Rykalin

9

)

The situation existing after arc extinction may be described as shown in Fig. 1.66. From time

t

=

t*

there is no net heat supply to the weldm ent. This cond ition is satisfied if the real source

q

0

is considered maintained by adding an imaginary source

+q

o

and sink

-q

o

of the same

strength at

t*.

The temperature at some later time

t**

in a given position

R

0

(measured from the

origin

0 )

is then equal to the difference of temp eratures due to the positive heat sources

q

o

and +q

o

and the negative heat sink -q

o

. Each of these temperature contributions will be a

product of a pseudo-steady state temperature

T

ps

,

and a correction factor K

1

or K

2

(given by

equations (1-49) and (1-82), respectively). Hence, for 3-D heat flow, we have:

(1-116)

(1-117)

where

Similarly, for 2-D heat flow, we get:

and

where

(r

o

is the position of the weld with respect to the imaginary heat source at time

f*

in the

x

y

plane).

Example (1.14)

Consider repair welding of a heavy steel casting with covered electrodes under the following

conditions:

Suppose that a 50mm long bead is deposited on the top of the casting. Calculate the tem-

perature in the centre of the weld 5 s after arc extinction.

Solution

The pseudo-steady state temperature for points located on the weld centre-line (i|/ = = 0) can

be obtained from equation (1-65). When

t**

-

t*

=5 s, we get:

Referring to

Fig.

1.67, the po sition of the weld with respect to the imaginary heat source at

time

f*

is 10mm, which gives:


36/45

Fig.1.67.Sketch of weld bead in Examp le 1.14.

a)

3-D heat flow

(b)

(C)

3-D heat f low

3-D heat f low

Fig. / .6#.Reco mm ended correction fa cto r/fo r some joint configurations; (a) Single V-groove, (b) Dou-

ble V-groove, (c)T-joint.


37/45

Moreover, the dimensionless times

T**

and

T**

-

x*

are:

and

At these coordinates, the correction factor K

1

is seen to be 1 and 0.62, respectively (Fig.

1.18).The tempera ture in the centre of the w eld 5 s after arc extinction is thus:

which is equivalent to

LlOJ Thermal conditions during

root

pass welding

During conventional bead-on-plate welding the angle of heat conduction is equal to 180 due

to symmetry effects (e.g. see Fig.1.23). In order to apply the same heat flow equations during

root pass welding, it is necessary to introduce a correction factor,/, which takes into account

variations in the effective heat diffusion area due to differences in the join t geometry. Taking

/equal to 1 for ordinary bead-on-plate welding (b.o.p.), we can define the net heat input of a

groove weld as:

9

(1-118)

Recomm ended values of the correction fa ct or /fo r some joint configurations are given in

Fig. 1.68.

Example (Ll5)

Consider deposition of a root pass steel weld in a double-V-groove with covered electrodes

(SMAW) under the following conditions:

Calculate the cooling time from 800 to 500

0

C (Ar

875

), and the cooling rate ( C R .) at 650

0

C

in the centre of the weld when the groove angle is 60.

Solution

The cooling time, Ar

875

, and the cooling rate, C R ., can be obtained from equation (1-68) and

(1-71),

respectively:

Cooling time, At

m


38/45

Cooling rate at 65 0

0

C

The above calculations show that the thermal conditions existing in root pass welding may

deviate significantly from those prevailing during ordinary stringer bead deposition due to

differences in the effective heat diffusion area. These results are in agreement with general

experience (see Fig.1.69).

1.10.8

Semi-empirical m ethods for assessment of bead m orphology

In fusion welding fluid flow phenomena will have a strong effect on the shape of the weld

pool. Since flow in the weld pool is generally driven by a combination of buoyancy, electro-

magnetic, and surface tension forces (e.g. see Fig. 3.10 in Chapter 3 ), prediction of bead mor-

phology from first principles would require detailed cons ideration of the current and heat flux

distribution in the arc, the interaction of the arc with the weld pool free surface, convective

heat transfer due to fluid flow in the liquid pool, heat of fusion, convective and radiative losses

from the surface, as well as heat and mass loss due to evaporation.

Over the years, a number of successful studies have been directed towards numerical weld

pool modelling, based on the finite difference, the finite element, or the control volume ap-

proach.

24

31

Although these studies provide valuable insight into the mech anisms of weld pool

development, the solutions are far too complex to give a good overall indication of the heat-

and fluid-flow pattern. The present treatment is therefore confined to a discussion of factors

affecting the nominal composition of single-bead fusion welds. This composition can be ob-

tained from an analysis of the amount of deposit

D

and the fused part of the base material

B,

from which we can calculate the mixing ratio

BI(B

+ D) or

D I(B + D).

M ethods have been

outlined in the preced ing sec tions for handling such prob lems by m eans of point or line source

mo dels. The following section gives a brief description of procedures which can be used for

predictions of the desired quantities in cases where the classic models break down, or where

the calculation will be too tedious.

1.10.8.1Am ounts of deposit and fused parent metal

The heat conduction theory does not allow for the presence of deposited metal. The rate of

deposition,dM

w

ldt, is roughly proportional to the welding current /, and is often reported as a

coefficient of deposition, defined as:

(1-119)

(1-120)

Since the area of deposited metal

D

is frequently wanted, we may write:

where p is the density, and

v

is the welding speed.


39/45

C

n

m

A

Q

5

s

Plate thickness:

Groove

angle:= 60

Heat input,

E

(kJ/mm)

Fig.

1.69.Comparison between observed and predicted cooling times from 800 to 500

0

C in root pass

welding of

steel

plates (groove preparation as in

Fig.

1.68 b)). Data from Akselsen and Sagmo.

34

Recommended values of

k'/p

for some arc welding processes are given in Table 1.7. In

practice , the deposition coefficient

k'/p

will also vary with current density and electrode stickout

due to resistance heating of the electrode. Consequently, the num bers contained in Table 1.7

are estimated averages, and should therefore be used with care.

Example (1.16)

Consider stringer bead deposition (S AW) on a thick plate of low alloy steel under the follow-

ing conditions:

Table

1 .7

Average rates ofvolumedeposition in arc welding. Data from Christensen.

32

Welding Process

k'/p

(m m

3

A

1

s

l

)

SMAW 0.3-0.5

GMAW, steel 0.6-0.7

GMAW, aluminium -0 .9

SAW, steel -0 .7


40/45

Calculate the mixing ratioBf(B+ D ) at pseudo-steady state.

Solution

The am ount of fused parent material can be obtained from equation (1-75). If we include an

empirical correction for the latent heat of melting, the dimensionless radius vector a

4 m

be-

comes:

This gives:

Similarly, the amount of deposited metal can be calculated from equation (1-120). Taking

ifc'/p equal to 0.7mm

3

A

1

s

1

for SAW (Table 1.7), we get:

The mixing ratio is thus:

Example (L 17)

Consider stringer bead deposition with covered electrodes (SMAW) on a thick plate of low

alloy steel under the following conditions:

Calculate the mixing ratio

BI(B

+

D)

at pseudo-steady state.

Solution

In this particular case the conditions for a fast m oving high pow er source are not met. Thus, in

order to eliminate the risk of systematic errors, the amount of fused parent metal should be

calculated from the general Rosenthal thick plate solution (equation (1-45)) or read from Fig.

1.21. When

T

c

=

T

m

(i.e. 8^ =

1),

we obtain:

Readin g from Fig. 1.21 gives:


41/45

and

Moreover, the amount of deposited metal can be calculated from equation (1-120). Taking

k'/p

equal to 0.4mm

3

A

1

s~

l

for SMAW (Table 1.7), we get:

and

The above calculations indicate a small difference in the mixing ratio between SA and

SMA welding, but the data are not conclusive. In practice, a value ofBI B+

D)

between 1/3

and 1/2 is frequently observed for SMAW, while the mixing ratio for SAW is typically 2/3 or

higher. The observed discrepancy betw een theory and experim ents arises probably from diffi-

culties in estimating the amount of fused parent metal from the point heat source model.

1.10.8.2

Bead penetration

It is a general experience in arc welding that the shape ofthefusion bound ary w ill depart quite

strongly from that ofasemi-circle due to the existence of high-veloc ity fluid flow fields in the

weld pool.

24

31

For combinations of operational param eters within the normal range of arc

welding, a fair prediction of bead penetration

h

can be made from the empirical equation

derived by Jacksonet

al.:

33

(1-121)

A summary of Jackson's da ta is shown in Table 1.8. It is seen that the constant C in equa-

tion (1-121) has a value c lose to

0.024

for SAW and SMA W with E6015 type electrodes, and

about

0.050

for GMAW with

C O

2

-shielding

gas.

Penetration measurements of GM A/Ar + O

2

,

GM A/Ar, and GM A/He welds, on the other hand, show a strong dependence of polarity, and

shielding gas composition, to an extent which m akes the equation useless for a general predic-

tion. Such data have therefore not been included in Table 1.8.

Example (1.18)

Based on the Jackson equation (equation (1-121)), calculate the bead penetration for the two

specific w elds considered in Examples (1.16) and (1.17). Use these results to evaluate the

applicability of the point heat source model under the prevailing circumstances.

Solution

From equation (1-121) and Table 1.8, we have:


42/45

Table 1.8Recom mend ed bead pen etration coefficients for some arc welding processe s. Data from

Jackson.

33

Welding Process C Comm ents

SAW, steel -0 .0 24 Various types of fluxes

Zzfrom 3 to 15 mm )

SMAW, steel -0.0 24 Wide range of /,

U,

and v

(E6015) (hfrom 0.7 to 5mm )

GMAW, steel -0 .05 0 Electrode positive

(C O

2

- shielding) (h from 6.5 to 8mm)

and

The corresponding values predicted from the point heat source model are:

and

Provided that the Jackson equation gives the correct numbers, it is obvious from the above

calculations that the point heat source m odel is not suitable for reliable predictions of the bead

penetration during arc welding. This observation is not surprising.

1.10.9

Local preheating

So far, we have assumed that the ambient temperature

T

0

rema ins constant during the w elding

operation (i.e. is independent of time). The use of a constant value of

T

0

is a reasonable ap-

proxima tion if the work-piece as a whole is subjected to preheating. In many cases , however,

the dimensions of the weldment allow only preheating of a narrow zone close to the weld.

This,

in turn, will have a significant influence on the predicted weld cooling programme, par-

ticularly in the low tem perature regime where the classic models eventually break dow n when

T

approaches

T

0

.

Model (after Christensen

n

)

The idealised preheating model is shown in Fig. 1.70. Here it is assumed that the weld centre-

line temperature is equal to the sum of the contributions from the arc and from the field of

prehea ting. The former contribution is given by equation (1-45) forR

=

-x

=

Vt,provided that

the plate thickness is sufficiently large to maintain 3-D heat flow. Similarly, the tem perature

field due to preheating can be calculated as shown in Sec tion 1.7 for uniaxial heat conduction

from extended sources (thermit we lding). By combining equations (1-45) and (1-22), we

obtain the following relation for the weld centre-line:

(1-122)


43/45

Temperature profile

att

= 0

Weld

Preheated

zone

T

z

Fig.1.70.Sketchof preheating model.

where T* is the local preheating tem pera ture, and L* is the half w idth of the pre hea ted zone.

Equation (1-122) can be written in a general form by introduc ing the following groups of par-

ameters:

Dimensionless temperature:

Time constant:

Dimensionless time:

Dimensionless half width of preheated zone:

(1-123)

(1-124)

(1-125)

(1-126)

(1-127)

By inserting these parameters into equation (1-122), we obtain:


44/45

e

Fig.

1.71.

Graphical representation of equation (1-127).

^ 6

It is evident from the graphical representation of equation (1-127) in Fig. 1.71 that the

predicted weld cooling programm e falls within the limits calculated for Q -^ 0 (no prehea ting)

and Q

/ 7

-> oo (global preheating). The con trolling param eter is seen to be the dimensionless

half width ofthepreheated zone Q , which depends both on the actual width L*, the base plate

thermal properties

a,

X, and the net heat input

q

o

Iv .

Example (1.19)

Consider stringer bead deposition with covered electrodes (SMAW) on a thick plate of low

alloy steel under the following conditions:

Calculate the cooling time from 800 to 50O

0

C (A%

5

), and the cooling time

1O

o measured

from the moment of arc passage to the temperature in the centre of the weld reaches 10O

0

C.

Solution

First we calculate the time constant

t

o

from equation (1-124):

from which we obtain


45/45

Cooling time, At

8/5

The dimensionless temperatures conforming to 800 and 500

0

C are:

Reading from Fig. 1.71 gives:

from which

This cooling time is only slightly longer than that calculated from equation (1-68) for T

0

=

20

0

C (6.9s), showing that moderate preheating up to 100

0

C is not an effective method of

controlling Ar

875

.

Cooling time, t

]0 0

When

T=T

0

*

=100

0

C, the dimensionless tem perature 9* = 1. Reading from Fig. 1.71 gives

T

6

- 10, from which:

The above value should be compared w ith that evaluated from the numerical data of Yurioka

et

al.,

35

replotted in Fig. 1.72 (see p.104). It follows from Fig. 1.72 that the weld coo ling

program me in practice is also a function of the plate thickness

d ,

an effect w hich canno t read-

ily be accounted for in a simple analytical treatment of the heat diffusion process. For the

specific case considered above the param eter ^

100

varies typically from 500 to 900s, depending

on the chosen value ofd.This cooling time is significantly shorter than that calculated from

equation (1-127), indicating that the analytical model is only suitable for qualitative predic-

tions.

References

1.

H.S . Carslaw and

J.C.

Jaeger:

Cond uction of Heat in Solids;

1959 , Oxford, Oxford University

Press.

2. British Iron and Steels Research Asso ciation: Physical Constants of some Co mm ercial Steels

at Selected Temperatures;1953, London, Butterworths.

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