shunting effect in resistance spot welding steels â€” part 2

Introduction

Shunting in resistance spot welding is the diversion of the weld-ing current from the weld to be made to a nearby existing weld(Ref. 1). If a significant proportion of welding current flowsthrough the previously made weld, the heat generated may not besufficient for making a weld of designated size. In general, shunt-ing may have significant influence on weld quality when makingmore than one weld on a workpiece, which is common in sheet

metal manufacture and repair. Quantitatively predicting the crit-ical weld spacing to avoid significant reduction in weld size due toshunting has practical significance (Ref. 1). The distribution ofwelding current in shunting is illustrated in Fig. 1. The proportionof the diverted current is determined by the relative electrical re-sistance values in the shunting and welding paths. Therefore, de-termination and control of relative resistance in welding are of ul-timate importance. Helped by the advances in numericalsimulation techniques, efforts have been made to analyze the ef-fect of shunting on weld nugget growth (Refs. 2–4), with some im-plication on the critical weld spacing. However, the highly variableand dynamic nature of electrical and thermal processes in weld-ing makes it difficult to quantitatively understand the effect ofshunting either by analytical analysis or numerical modeling. Be-cause of a serious lack of material properties, especially as func-tions of temperature, a numerical modeling of the resistance spotwelding process generally relies on idealized material behaviorsand process setup. As a result, numerical predictions are morequalitative than quantitative, and empirical studies such as theones by Howe (Ref. 5) and Wang et al. (Ref. 6) have been domi-nant in shunting study.

The limitations of empirical investigations are apparent. Firstof all, it is difficult to identify or isolate the influence of any indi-vidual variable as there are a large number of variables involvedand extensive interactions exist among them in shunting. All of thewelding parameters, i.e., welding current, time, and electrodeforce, and material properties such as bulk resistivity and surfaceconditions impact shunting to a more significant and complex ex-tent than they do in making a single spot weld. In addition, otherfactors of a more random nature such as electrode wear, electrodealignment, and workpiece fitup may also affect the shuntingprocess. Considering all these effects would make an experiment

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Shunting Effect in Resistance Spot WeldingSteels — Part 2: Theoretical Analysis

Minimum weld spacing can be quantitatively predicted based on the process parameters and welding schedules

BY Y. B. LI, B. WANG, Q. SHEN, M. LOU, AND H. ZHANG

ABSTRACT

Shunting is a phenomenon difficult to avoid in productionwelding, and it is of practical interest to quantitatively determinethe minimum weld spacing. However, the large number of fac-tors involved in shunting make it difficult to isolate their influ-ence, let alone obtain a quantitative understanding of their ef-fects. In this study, the shunting process was understood throughan analysis of the electrical resistances along the welding andshunting paths. An analytical model was derived based on theequivalence of the joule heat generated in welding and that wasneeded to create the weldment. The constants in the model weredetermined through experiments. Using the experimental re-sults from a previous study, specific models were derived for sev-eral gauges of mild and dual-phase steels of various surface con-ditions. The models were then used to study the effects of processparameters on the minimum weld spacing needed to create cer-tain sizes of shunted welds. The critical or minimum weld spac-ing was then plotted as a function of several variables. The ef-fects of several process variables such as electrode force, weldingtime, shunt weld size, and sheet thickness on shunting wereclearly demonstrated. Such relationships are crucial in under-standing the effects of process variables on shunting, and can beused in quantitative determination of minimum weld spacing toavoid the adverse effect of shunting and put as many welds aspossible onto a structure.

KEYWORDS

Critical Weld SpacingShuntingResistance Spot WeldingModel Development

Y. B. LI, Q. SHEN, and M. LOU are with Shanghai Jiao Tong University, Shanghai, China. B. WANG is with Zhejiang Normal University, Jinhua, China.H. ZHANG ([email protected]) is with University of Toledo, Toledo, Ohio.

Fig. 1 — Schematic of shunting in resistance spot welding.

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matrix too complex to handle. As revealed in the work by Wang etal. (Ref. 6), many material and processing factors such as the elec-trode force affect shunting, and their effects also strongly dependon the values of other variables: increasing the electrode force re-duces shunting when the weld spacing is large, while it actuallypromotes shunting when the weld spacing is small when weldingthin sheets. The large number of variables and their complicatedinteractions also make it difficult to obtain an accurate account ofthe influence of an individual factor through experiments alone.On the other hand, theoretical analysis is difficult considering thenumber of variables involved and the limited knowledge on thematerial properties governing the physical processes during weld-ing, especially their dependence on temperature, which makesshunting a very dynamic process. In this study, an analytical modelwas developed based on the understanding of the physicalprocesses involved in shunting, and the numerical values of the co-efficients in the model were derived from the experimental resultsobtained in a previous study (Ref. 6).

Modeling of the Shunting Process

As resistance spot welding is basically a joule heating process,an understanding of shunting can be achieved through an analy-sis of the electrical resistances involved in the process. A commonwelding mode in industrial applications, constant current weldingmode was assumed in the model development. For simplicity onlythe nearest neighboring weld was considered, and the influence ofall other welds was assumed negligible. The electrical process ofshunting is readily represented by flowing electric current througha simple electric circuit, identical to that in Fig. 2 in Ref. 6, con-sisting of several resistors based on the effects of various portionsof the sheet stack-up on heat generation and electric current flow,which can be derived from the schematic in Fig. 1. First, the con-tact resistance at the electrode-sheet interface could be significantin affecting the welding process. However, it can be assumed iden-tical for the weld being made (the shunted weld) and its shunt weldand, therefore, its effect can be ignored for simplicity and it canbe excluded in the study of the shunting effect. As a result, thenumber of resistances needed to be considered in developing theshunting model is reduced, and they can be classified according totheir contributions to welding and shunting, along their respectivepaths.

The electrical resistance to the shunting current IS, in the paththrough the previously made weld (shunt weld) can be assumed tobe dominated by bulk resistance, and approximated as

where L2 = D2 + t2, and the dimensions are illustrated in Fig. 1. Dis the horizontal projection of the shunting current path L. Itsvalue can be assumed as

Spacing – αd0 – βdI

where Spacing is the distance between the centers of the shunt and

shunted welds (marked as “Weld Spacing” in Fig. 1), α and β areconstants used to specify the ends of the shunting path betweenthe shunt weld and the indentation impression mark. These twoconstants would assume a value of 0.5 if the shunting current flewdirectly from the edge of the indentation mark to the edge of theshunt weld, which is the shortest path as can be seen in Fig. 1. Themetallography in Fig. 2 of welds made on a 2.0-mm mild steelsheet with 8-mm weld spacing from an experimental study ofshunting (Ref. 6) shows they should be slightly smaller than 0.5.From the figure it can be seen that the outlines of the heat-affected zones (HAZ) of the shunted welds are asymmetric, indi-cating uneven heating during welding. The HAZ of a shuntedweld has upper and lower left corners extending to the electrodecontact surfaces, which are different from those on the right side,indicating possible concentrated electric current passing throughthese areas. Similar phenomenon has been observed in othershunting welds in experiments (Ref. 6). Consider the upper leftcorner of the HAZ in the first shunted weld (the second in the se-quence) in Fig. 2. As the darkened area near the electrode surfaceis located inside the edge of the indentation mark, it is reasonableto assume that the shunting current path starts from this place, notthe indentation edge. For the same reason the center of the shunt-ing path is assumed passing through a point inside the shunt weld,not on its edge. Considering the possible shunting path revealedby this figure, the vertical projection of the shunting path shouldalso be slightly smaller than 2t as exhibited in Fig. 1. Because ofthis, γt instead of t, where γ is smaller than unity should be usedfor calculating L, i.e.,

L2 = (Spacing – αd0 – βdI)2 + (γt)2

The average cross-sectional area of the shunting path, AS, can beassumed to be proportional to the average of the projected areasof the shunt weld and the electrode indentation onto the shuntingpath, i.e.,

where θ is as shown in Fig. 1. As sinθ≈t/L, the bulk resistance ofthe shunting path is

The influence of other possible factors on RbS can be assumedunchanged during shunting, and lumped into a constant CbS forquantifying the bulk resistance of the shunting path

R L

AbS bulkS

∝ρ2

A d d d dS I I

∝ +⎛

⎝⎜⎜

⎞

⎠⎟⎟ = +

⎛1 1 1 1

2 41

4 802 2

02 2π π θ πsin

⎝⎝⎜

⎞⎠⎟sinθ

R L

d d t

Spacing d

bS bulk

I

bulk∝

+⎛⎝⎜

⎞⎠⎟

=− −

ρ ρα2

02 2

0ββ γd t

d d t

I

I

( ) +( )+

⎛⎝⎜

⎞⎠⎟

2 2

02 2

Fig. 2 — Cross-sectional views of the shunt and shunted welds made on 2-mm bare mild steel, with 8-mm weld spacing. The shunted welds were madewith a PVC plastic film placed on the faying interface. The welding parame-ters were welding current = 6 kA, welding time = 500 ms, and electrode force= 2.8 kN.

Fig. 3 — Schematic of loading on half of the sheet stack-up approximated asa cantilever beam, with one end “fixed” by the shunt weld.

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As the original faying interface is eliminated in the shunt weld,the contact resistance in the shunting path can be assumed to bezero. The bulk resistance of the welding path can be derived in asimilar manner as RbS:

The cross-sectional area of the welding path can be approxi-mated by the average of the contact area at the faying interface(or the projected area of the shunted weld), and that at the elec-trode-sheet interface

And RbW can be written as the following, with a constant CbW forthe effect of all other fixed variables

The contact resistance at the faying interface in the weldingpath can be assumed to stem from a cylinder of a mixture, here-after called “contact cylinder,” of the bulk metal and the sub-stances/contaminants on the surfaces. This cylinder has a heightof lo and cross-sectional area of AW, which is a function of the ap-plied electrode force. The contact resistance is affected by theelectrode force squeezing the weld stack-up, and such effect is re-flected by the deformation of this contact cylinder, approximatedas σy/σappl × lo. A base metal with a high yield stress, σy, resiststhe deformation and reduction of electrical resistance; a largeelectrode force generates a large applied stress at the faying in-terface, σappl, and reduces contact resistance. Therefore, the con-tact resistance at the faying interface, RcW, based on the afore-mentioned discussion, can be assumed

The constants CcW1 and CcW2 can be regarded as the weight-ing factors of the contributions from the bulk and surface resist-ances in the contact cylinder. They contain the effects of surfacecontaminants, other surface characteristics such as roughness andcoating, and the contact cylinder height. The net force exerted onthe faying interface at the shunted weld, resulting from the appliedelectrode force, is Fappl = σapplAW, and the contact resistance cantherefore, be expressed as

The net force at the faying interface, Fappl, is usually smallerthan the electrode force. Although it is difficult to accurately cal-culate its value, it can be estimated through a structural analysisof the forces acting on the welding stack-up.

By considering the top sheet as a cantilever beam “fixed” on

the left by the shunt weld when the shunted weld is being made asshown in Fig. 3, the actual force at the faying interface, Fappl, isdifferent from the applied electrode force, Felectrode, because ofthe resistance of the top sheet to bending. This is similar to ananalysis of expulsion in resistance welding by estimating the netforce exerted by the electrodes at the faying interface (Ref. 7). Ap-proximating the top (or bottom) sheet as a cantilever beam allowsfor an estimate of the force at the faying interface that is respon-sible for affecting the contact resistance when making the shuntedweld. Through an analogy to the maximum deflection under a con-centrated loading as formulated in any fundamental structuralanalysis such as Ref. 8, the following relation can be derived forthe configuration in Fig. 3:

The coefficient η represents the influence of the sheet widthand material strength. Therefore, the contact resistance at the fay-ing interface along the welding path can be expressed as

Considering the electric circuit consisting of the shunting andwelding paths, the shunting current IS can be related to the over-all current in the secondary loop, I, in the form of

From this equation it can be seen that a large resistance of theshunting path reduces the value of shunting current and, there-fore, the shunting effect. The welding current is expressed in asimilar way as

The dependence of the shunted weld on the shunt weld size,welding time, current, and electrode force, in addition to the sheetthickness and strength, can be derived by considering the equiva-lence of heat needed for making the shunted weldment and theheat generated through joule heating along the welding path.

The shunted weldment can be divided into two parts, and dif-ferent amounts of heat are needed to create them. One is the weldnugget. It can be approximated by an ellipsoid with a volume

where λ is a constant, representing the ratio of the height of theellipsoid nugget to its diameter. On the other hand, the joule heatis also consumed to generate the HAZ, the volume of which canbe approximated by the difference between a cylinder of size

R C CAcW cW bulk cW conty

appl W

= +( )1 2ρ ρ

σ

σ

R C CFcW cW bulk cW cont

y

appl

= +( )1 2ρ ρ

σ

F F t

Spacing dappl electrode

= −

−( )η

3

00.5

3

R C C

F t

Sp

cW cW bulk cW conty

electrode

= +( )−

1 2 3ρ ρ

σ

η

aacing d−( )0.5

(3)

0

3

A d dbW I

= +⎛

⎝⎜⎜

⎞

⎠⎟⎟

1

2

1

4

1

42 2π π

R C t

d dbW bW bulk

I

=+

ρ2 2

(2)

R CSpacing d d t

d dbS bS bulk

I

I

=− −( ) +( )

+ρ

α β γ0

2 2

02 2⎛⎛

⎝⎜

⎞⎠⎟t

(1)

R t

AbW bulkbW

∝ρ2

IR R

R R RIS

bw cw

bS bW cW=

+

+ +(4)

IR

R R RIW

bs

bS bW cW=

+ +(5)

4

3 2 2

1

33π λ πλ

d d d d⎛

⎝⎜⎜

⎞

⎠⎟⎟

⎛

⎝⎜⎜

⎞

⎠⎟⎟( ) =

24 2

2 2t d td( )⎛

⎝⎜⎜

⎞

⎠⎟⎟=

ππ

1



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and that of the nugget. Therefore, the total heat needed for theshunted weldment is approximately

In the above expression, the coefficients on the left-hand siderepresent the unit heats needed for making the nugget and theHAZ, and they can be lumped up as on the right-hand side forconvenience.

The heat needed comes from resistance heating, and usingEquation 5 the joule heat can be expressed as

Here τW is the welding time and I is the total welding currentused when making the shunted weld. Equating the joule heat tothat needed for making the weld produces the relationship be-tween the shunted weld size and the welding parameters, materialproperties, and premade shunt weld size:

Although Equation 6 is derived using several assumptions andsimplifications, it outlines the fundamental relationship amongthe variables when welding with a shunt weld. Welding spacing, asan important welding process parameter, can be determined usingthis relation. In addition, it provides a quantitative guidance forselecting welding parameters in order to achieve quality weldsunder restraints of weld spacing, as often seen in engineering de-sign of welding. The constants in Equation 6 have to be deter-mined through carefully planned experiments for practical use.

Examples

The model shown in Equation 6 relates the shunted weld to theshunt weld and other process variables. However, the materialproperties and process parameters are not sufficient, even if theyare available, to determine the constants in the model. The influ-ence of the unavoidable random factors as well as the large num-ber of assumptions and simplifications made when deriving the

model make accurate analytical calculation of the constants irrel-evant. The constants in Equation 6, however, can be determinedand the equation explicitly expressed using the experimental re-sults such as those obtained in Ref. 6.

Before fitting the equation using the experimental observa-tions, a simplification is necessary on the constants of Equation 6.First, both α and β can be chosen as 0.495, so the shunting currentpath extends just slightly into the electrode impression mark andthe shunt weld, as illustrated in Fig. 1. Similarly, γ can be taken as0.95. As the accurate bulk and contact resistivity values are gen-erally difficult to obtain, their effects can be better represented bylumped coefficients, determined through curve fitting using ex-perimental results that are categorized according to the surfaceconditions. Standard curve fitting procedures such as those pro-vided by commercial software packages can be used in the calcu-lation. Equation 6 can be simplified, by consolidating the coeffi-cients, as

The constants in Equation 7, c1, c2, c3, c4, c5, c6, and c7, can bedetermined through experiments with sufficient replications andas many combinations of variables as possible. They are clearlymaterial dependent, and the surface condition plays an importantrole in affecting the values of these constants. It should be notedthat although the model shown in the equation is generic, a fittedmodel developed for a specific material system should be limitedto that material in the ranges of the relevant material properties.

To illustrate the procedure of determining the constants andthe use of the model in understanding shunting, the experimentalobservations in a previous study (Ref. 6) were used to obtain theexplicit models for the material systems studied. The experimentsinclude two types of materials: mild steel (MS) and dual-phasesteel (DP) of several gauges. Several types of surface conditionswere used, including bare steel surface, pure zinc-coated or hot-dipped galvanized (HDG) surface, plastic insertion of a thinpolyvinyl chloride (PVC) film, and their combinations. Because ofthe overwhelming influence of the contact resistance the experi-mental data were classified into four groups according to the sur-face conditions at the faying interface for the shunted welds: baresteel surface (MS), zinc-coated (HDG) surface, bare steel (MS)+ plastic insert, and zinc-coated (HDG) + plastic insert. The val-ues of these four types of contact resistances are expected to bevery different, in addition to being unknown. Therefore, they weretreated separately to avoid complications and inaccuracy in quan-tifying the shunting relations using Equation 7.

The constants in the equation were determined through curvefitting using Mathematica8™ (Ref. 9) for each of the four types ofsurface conditions. A fixed size of electrode indentation, dI, taken

′ + ′ =

++ +

c d c td I

C t

d dC

n h W

bW bulkI

cW bulk

3 2 2

2 2 1

τ

ρ ρ CC

F t

Spacing d

cW cont

y

electrode

2

3

0.5

ρ

σ

η

( )

−

−( )0

33

⎛

⎝

⎜⎜⎜⎜⎜⎜⎜⎜⎜

⎞

⎠

⎟⎟⎟⎟⎟⎟⎟⎟⎟

•

−C

Spacing d

bS bulkρ

α00

−( ) +( )+

⎛⎝⎜

⎞⎠⎟

β γ

ρ

d t

d d t

CSpacin

I

I

bS bulk

2 2

02 2

gg d d t

d d tC tI

I

bW bulk

− −( ) +( )+

⎛⎝⎜

⎞⎠⎟

+α β γ

ρ0

2 2

02 2 dd d

C C

F

I

cW bulk cW conty

electrode

2 2

1 2

+

+ +( )−

ρ ρσ

ηtt

Spacing d

3

0

30.5−( )

⎛

⎝

⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜

⎞⎞

⎠

⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟

2

(6)

I R R IR

R R RR

W bW cW WbS

bS bW cWbW

2 2

2

+( ) =+ +

⎛

⎝

⎜⎜

⎞

⎠

⎟⎟τ ++( )R

cW Wτ

c d c td d cn h

1

3

1

2

1

33 2 3πλ π πλ

⎛

⎝⎜⎜

⎞

⎠⎟⎟+ −

⎛

⎝⎜⎜

⎞

⎠⎟⎟= ′

nn hd c td3 2+ ′

c d c td d d t

ct

I13

22

02 2

22

3

20.95

+⎛⎝⎜

⎞⎠⎟ +⎛⎝⎜

⎞⎠⎟

( ) + SSpacing d d

d d t

c

I

I

− −( )+

⎛⎝⎜

⎞⎠⎟

+

0.495 0.4952

02 2

0

44 2 2 46

73

0.

c t

d dc

c

Fc t

Spacing

I

y

electrode

5

++

−

−

σ

55

0.95

0

3

2

2

d

IW

( )

⎛

⎝

⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜

⎞

⎠

⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟

= τ tt Spacing d d

c

I( ) + − −( )⎛

⎝⎜⎜

⎞

⎠⎟⎟

2

0

22

5

0.495 0.495

tt

d d

c

Fc t

Spacing d

I

y

electrode

2 2

6

73

00.5

++

−

−( )

σ

33

⎛

⎝

⎜⎜⎜⎜⎜⎜⎜⎜

⎞

⎠

⎟⎟⎟⎟⎟⎟⎟⎟

( )7



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as 5.0 mm from the experiments, was used in the curve fitting. Incurve fitting, the physical meaning of the constants should not besacrificed for the closeness of numerical fitting. For instance, anegative c7 produces a better numerical fitting than a positive one.However, it makes no physical sense according to the analysis inthe previous sections on the cantilever beam as demonstrated inFig. 3. In the present study, certain conditions were imposed onsuch coefficients in order to preserve their physical meaning. Theconstants determined for the four types of surface conditions arelisted in Table 1.

The values of the constants in the table vary in drastic ranges.The main reason is that the units of the variables in Equation 7were not made consistent, for the convenience of practical weld-ing. For instance, the unit of sheet thickness in the equation is mil-limeter while that of the yield strength of material is MPa. Thiscan be observed by comparing the coefficients c3 and c6, while theformer is for the dimensions, with a large value, and the latter cor-responds to pressure with a much smaller value.

The accuracy of the models in Table 1 was verified by compar-ing the two sides of Equation 7. Very small differences betweenthe values of the two sides were obtained for all the sets of exper-imental observations and, therefore, the models were consideredvalid. The fitted models shown in Table 1 can be used to study theinfluence of various parameters. As weld spacing is the most im-portant parameter in weld design, it was expressed in this study asa function of other variables. The weld spacing needed to obtaina shunted weld of certain size was expressed as a percentage of theshunt weld size, in order to meet the requirements of weld qual-ity, mainly in terms of weld size, in practice.

Effect of Sheet Thickness

Figure 4 shows the required weld spacing to achieve a certainsized shunted weld goes up with sheet thickness. As expected, alarge weld spacing is necessary in order to have a shunted weld ofsize close to that of the shunt weld. For 0.5-mm bare mild steels,an increment of little more than 1 mm is needed when the shuntedweld size goes from 70 to 85%, and then 100% of that of the shuntweld, as seen in Fig. 4A. Such an increment is more than 3 mm forthe 3-mm sheets. A greater increase in weld spacing is necessarywhen a plastic film was inserted in the faying interface. The plasticinsertion clearly raises the contact resistance and, therefore, theelectrical resistance along the welding path, amplifying the shunt-ing effect. However, this effect is thickness dependent. For thinsheets, a larger weld space is necessary for the bare steels than forthose with a plastic insert, and the latter overtake the former whenthe sheet thickness goes beyond the range of 1.5–1.7 mm. In gen-eral, shunting is more sensitive to sheet thickness when the plasticinsert is used, implying that the contact resistance along the weld-ing path plays a decisive role in shunting. A sizeable difference ex-ists between these two types of interfaces for thick sheets as well.For instance, the 3-mm sheet with plastic insert needs a weld spac-ing of 45 mm, 12 mm larger than that without the plastic insert.

Similar to that observed in the MS, the weld spacing goes upwith sheet thickness for both zinc-coated and zinc-coated + plas-

tic insert when welding DP steels — Fig. 4B. The effect of plasticinsert in HDG DP steels is not as significant as in the MS. Thiscould be the result of a nullified influence of the zinc coating bythe plastic film.

Effect of Welding Time

In Fig. 5, the shunt weld size was fixed at 4.8 mm for a 1.5-mmMS. It shows that increasing welding time is an effective means ofminimizing the effect of shunting as it puts more heat into a weldand reduces the weld spacing needed. When welding time is short,the time to melt the interface takes a significant proportion of theentire welding time. The electric current diverted by the shuntweld results in a large percentage of heat loss, and a large weldspacing is necessary in order to avoid shunting. With a long weld-ing time, however, it takes a small fraction of the total time for thecontact resistance to disappear when the interface melts, andmore current and heat are distributed to the shunted weld as a re-sult. This effect is more profound when the plastic insert is usedat the faying interface. The diversion of electric current from thewelding path into the shunting path is magnified by the plastic in-

Table 1 — Constants of Equation 7 for the Materials with the Four Types of Surface Conditions Tested in the Experiments

Mild steel (bare) Mild steel (bare) + plastic insert DP steel (HDG) DP steel (HDG) + plastic insert

c1 1.22239 × 10–9 8.93766 × 10–14 2.37641 × 10–9 3.32993 × 10–9

c2 3.08145 × 10–17 2.68256 × 10–9 1.73576 × 10–12 4.75207 × 10–15

c3 378747.0 492327.0 240506.0 526676.0c4 158244.0 329371.0 169569.0 23620.0c5 0.893066 0.0868412 0.0916093 3100.98c6 0.892577 0.0868538 0.0918372 2.927c7 0.999269 1.00023 1.00044 772.487

Fig. 4 — Effect of sheet thickness on weld spacing: A — Of the mild steel withd0 = 4.8 mm, I = 6 kA, σy = 205 MPa, F = 2.3 kN, τ = 350 ms; B — of theHDG DP steel with d0 = 5.9 mm, I = 8 kA, σy = 665 MPa, F = 4.0 kN, τ = 500 ms.

A

B



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sert when welding time is short, and less heat is directed to theshunted weld, resulting in a larger weld spacing necessary than ina bare steel. When the welding time is long, however, the in-creased contact resistance from the plastic insert actually works tothe benefit of reducing weld spacing because more heat is gener-ated at the shunted weld compared with the case of bare steel. Thisexplains that the weld spacing needed for welding with the plasticinsert is significantly smaller than that without the plastic insert.

Effect of Electrode Force

Comparing Fig. 6A with Fig. 5, it can be seen that the influenceof electrode force on weld spacing is similar to that of weldingtime. A large electrode force reduces the contact resistance in thewelding path, as can be seen from Equation 3. Therefore, a smallweld spacing is allowed with large electrode forces. Figure 6 alsoshows the electrode force has a smaller effect when the plastic in-sert was used at the faying interface. This is related to the way theplastic-inserted interface evolves during welding. Under a large

electrode force, a certain amount of (molten) plastic is “sealed”by the electrode force exerted at the faying interface, and thisamount doesn’t change much with increasing electrode force. Asa result, the contact resistance is largely determined by the “en-trapped” polymer, and the electrode force, which is the dominantfactor on steels without plastic insert, is less effective in creatingan intimate contact between the two sheets. Therefore, with theexistence of plastic film at the interface, the electrode force has alesser effect compared with that of a bare interface.

It is interesting to see that in the DP steels, the dependence ofweld spacing on electrode force shows similar trends in the HDGand HDG + plastic insert specimens. With a loose requirementof the shunted weld reaching 70% of the shunt weld in size, theplastic insert makes negligible difference. When making largershunted welds, however, the difference in weld spacing betweenthose of the original HDG and plastic-inserted HDG faying in-terfaces goes up, yet the difference is virtually a constant. There-fore, the influence of electrode force on weld spacing is similarwith these two types of contact interfaces. This appears related tothe zinc coating. The existence of pure zinc on the surface reducesthe contact resistance, while inserting a plastic film at the fayinginterface does the opposite. Increasing the electrode forcesqueezes some of the molten zinc out of the contact area to its pe-riphery. But this part of the zinc still contributes to conductingelectric current along the welding path, as it accumulates along theperiphery of the contact area, forming a ring of molten zinc.Therefore, increasing the electrode force has a smaller effect onchanging the contact resistance, resulting in a smaller decrease inweld spacing as shown in Fig. 6B than observed in the uncoatedmild steels in Fig. 6A. The increased joule heating, along with a

corresponding decrease in weld spacing, results from a decreasein contact resistance and an increase in welding current when in-creasing the electrode force on the original zinc-coated interface.A similar process could occur in the plastic-inserted stack-up. Thelarger contact resistance with the plastic insert generates moreheat compared to the one of original surfaces, and results insmaller weld spacing when making similar sized welds.

Effects of Other Factors

As several DP steels of different grades were used in the ex-periment, the yield strength can be regarded as a variable. Theweld spacing requirements as functions of yield strength from 300to 900 MPa are plotted in Fig. 7. Similar to the dependence of weldspacing on other variables in the HDG DP steels, the yieldstrength of the sheet material has a smooth effect on the weldspacing. Increasing the yield strength results in an increase in weldspacing at a fixed electrode force, as a sheet with a large yieldstrength is less compliant and a small intimate contact is producedat the faying interface. However, such an intimate contact has asmaller impact on the overall contact resistance in HDG steels, asthe molten zinc can easily fill the root opening at the faying inter-face. A larger rise in weld spacing should be expected when weld-ing bare steels.

The horizontal projected length and, therefore, that of theshunting path decrease when the shunt weld size increases as seenin Fig. 1. The actual shunting path and, therefore, the shunting ef-fect change along with the shunt weld even with fixed weld spac-ing. Figure 8 shows the dependence of weld spacing on the shuntweld size in order to achieve a certain sized shunted weld. As ex-pected, weld spacing increases with the shunt weld size, and forthe same sized shunt weld a larger shunted weld requires a largerweld spacing.

The combined effect of the electrode force and welding timeon weld spacing can be presented using a contour plot as shown

Fig. 5 — Dependence of weld spacing on welding time for the mild steel withd0 = 4.8 mm, I = 6 kA, σy = 205 MPa, F = 2.3 kN, t = 1.5 mm.

Fig. 6 — Effect of electrode force on weld spacing: A — Of the mild steel withd0 = 4.8 mm, I = 6 kA, σy = 205 MPa, t = 1.5 mm, τ = 350 ms; B — of theDP steel with d0 = 5.9 mm, I = 8 kA, σy = 665 MPa, t = 1.2 mm, τ = 500 ms.

A

B


in Fig. 9. For this bare steel, both the electrode force and weldingtime reduce the weld spacing needed to produce a weld of thesame size as the shunt weld. Increasing either electrode force orwelding time individually can shorten the weld spacing from ap-proximately 32 to 26 mm, and simultaneously raising these twowelding parameters to 3.0 kN and 500 ms, respectively, may ren-der an identical-sized weld to the shunted one with a weld spac-ing of only 21 mm.

When a plastic film was inserted into the faying interface whenmaking the shunted weld, the effects of electrode force and weld-ing time on the required weld spacing were different from thoseobserved in welding bare steels. In Fig. 10, a long welding time re-duces the weld spacing, which is similar to what was observed inFig. 5, while the weld spacing is fairly insensitive to the electrodeforce. This observation is consistent with that in Fig. 6A, where in-creasing electrode force is no longer effective in reducing weldspacing when the electrode force reaches a certain level. Thelargest weld spacing appears at the corner of maximal electrodeforce and minimal welding time. The different roles the electrodeforce plays in welding bare and plastic insertion-filled faying in-terfaces are the result of the containment of the plastic film in thecontact area by the electrode force, as discussed in the previoussection on the effect of electrode force. As the plastic insertionrepresents an extreme of contaminated sheet surfaces that is notnormally encountered in practice, the trend, rather than the value,of the weld spacing shown in the figure is more important. Manyof the surface contaminates such as grease, etc., may disappearunder the intensive heating in resistance spot welding and, there-fore, their influence on weld spacing is more suitably representedby Fig. 9 than Fig. 10.

Weld Spacing Requirements

In welding design, it is often necessary to determine the weldspacing as a function of sheet thickness. In Fig. 11, the weld spacingneeded for different gauges of MS and zinc-coated DP steels is plot-ted, in order to create a shunted weld of the same size as the shuntweld. Note that different welding parameters are used for predict-ing the weld spacing in these two types of materials, based on the ac-tual values obtained from the experiments. For the ease of use inwelding practice step functions were created. It shows that the weldspacing required for welding the MS is larger than that for the DPsteel, largely due to the difference in the surface resistance betweenthe steels used in the experiments. The MS steel was uncoated in fab-ricated condition, while the DP steels were hot-dip coated with zinc.A faying interface covered by pure zinc has significantly lower elec-trical resistance than that of a bare steel. As a result, the current inthe shunting path takes a smaller portion than in a bare steel stack-up. Therefore, the weld spacing required to avoid shunting in thecoated steel is smaller than in the bare steel. This effect is offsetslightly, though, by the yield strength of the DP steels, because a steelof higher yield strength usually requires a larger weld spacing as ittakes more electrode force to create an intimate contact at the fay-ing interface. For a fixed electrode force, a large weld spacing is re-quired when the material is strong, as seen in Fig. 7.


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Fig. 7 — Effect of sheet yield strength on weld spacing in HDG steels. d0 =5.9 mm, I = 8 kA, F = 4.0 kN, t = 1.2 mm, τ = 500 ms.

Fig. 8 — Effect of shunt weld size on weld spacing in bare MS steels. σy = 205MPa, I = 6 kA, F = 2.3 kN, t = 1.5 mm, τ = 350 ms.

Fig. 9 — Contour plot ofweld spacing vs. electrodeforce and welding time for abare mild steel. d0 = 4.8mm, σy = 205 MPa, I = 6kA, t = 1.5 mm, and theshunted weld size is identi-cal to that of the shunt weld.

Fig. 10 — Contour plotof weld spacing vs. elec-trode force and weldingtime for a bare mild steelwith a plastic insert atthe faying interface: d0= 4.8 mm, σy = 205MPa, I = 6 kA, t = 1.5mm, and the shuntedweld size is identical tothat of the shunt weld.


Summary

In this study, the shunting process was analyzed and an analyt-ical model was produced. Using the models for several materialsystems developed by fitting the experimental observations, theinfluences of several factors on the minimum weld spacing wereexplicitly and quantitatively expressed. The important findings aresummarized as follows:

1. The analytical model fits well with the experimental resultson all four types of drastically different surface conditions for themild and dual-phase steels of various gauges;

2. For all the factors considered, without exception, a largeweld spacing is always needed in order to make a large shuntedweld;

3. In general, the required minimum weld spacing goes up withthe sheet thickness, and a high contact resistance at the faying in-terface amplifies this dependence;

4. The effect of electrode force is accurately accounted for inthe analytical model by considering the net force at the faying in-terface. In general, it reduces the weld spacing required. However,its effect on weld spacing is affected by other factors, such as thesurface condition;

5. Welding time is effective in reducing weld spacing, and anexcessive contact resistance such as generated by inserting a plas-tic film at the faying interface may help in minimizing the weldspacing by generating more heat at the shunted weld;

6. The models also allow for an understanding of the effect ofsheet yield strength. A sheet of high yield strength requires a largeweld spacing because of its high resistance to deformation underan electrode force;

7. The size of the shunt weld directly affects shunting as it dic-tates the shunting path;

8. Contact resistance plays a dominant role in shunting, andzinc-coated surfaces generally behave significantly different thanbare steels;

9. The models also reveal the complex interactions among theprocess parameters in affecting shunting. For instance, the elec-trode force and welding time interact with the surface contact re-sistance in affecting shunting. Such an interaction is prevalent inshunting.

Through a carefully planned experiment, this analytical modelcan be used to describe the influence of process parameters onshunting in resistance spot welding a specific material. The con-clusions derived, however, are only applicable to the material sys-

tems in the range of experiment. Extrapolation is not recom-mended, especially in the cases of large variation in contact re-sistance.

Acknowledgment

Author B. Wang gratefully acknowledges the financial supportfrom Zhejiang Provincial Natural Science Foundation of P.R.China (Project No. LQ12E05006).

References

1. Tumuluru, M. D., Zhang, H., and Matteson, R. 2011. Procedure de-velopment and practice considerations for resistance welding. ASM Hand-book on Welding (Volume 6). Materials Park, Ohio: ASM International.

2. Chang, H. S. 1990. A study on the shunt effect in resistance spotwelding. Welding Journal 69(8): 308-s to 317-s.

3. Tsai, C. L., Dai, W. L., Dickinson, D. W., and Papritan, J. C. 1991.Analysis and development of a real-time control methodology in resist-ance spot welding. Welding Journal 70(12): 339-s to 351-s.

4. Browne, D. J., Chandler, H. W., Evans, J. T., James, P. S., Wen, J.,and Newton, C. J. 1995. Computer simulation of resistance spot weldingin aluminum (Part 2). Welding Journal 74(12): 417-s to 422-s.

5. Howe, P. 1994. Spot weld spacing effect on weld button size. Pro-ceedings of Sheet Metal Welding Conference VI, Paper C03. AWS DetroitSection.

6. Wang, B., Lou, M., Shen, Q., Li, Y. B., and Zhang, H. 2013. Shunt-ing effect in resistance spot welding steels — Part 1: Experimental study.Welding Journal 92(6): 182-s to 189-s.

7. Zhang, H., and Senkara, J. 2012. Resistance Welding: Fundamentalsand Applications. CRC Press/Taylor & Francis Group, 2nd edition, BocaRaton, London, New York.

8. Gere, J. M., and Timoshenko, S. P. 1997. Mechanics of Materials,PWS Publishing Co.

9. Mathematica 8, Wolfram Research, Inc., v. 8.0.1.0, Copyright1988–2011.


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Fig. 11 — Weld spacing as a function of sheet thickness. The shunted weld isassumed to have an equal size to the shunt weld. For the MS, d0 = 4.8 mm,σy = 205 MPa, and the welding parameters are I = 6 kA, τ = 350 ms, and F= 2.3 kN; and for the hot-dipped DP steels, d0 = 5.9 mm, σy = 665 MPa,and the welding parameters are I = 8 kA, τ = 500 ms, and F = 4.0 kN.

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