Sabbatical Leave Taken Fall 2015 Intelligent Integration ... H-Fall 2015.pdfOn the sheet metal optimization project, I and my colleagues in China have finished the development of general

Sabbatical Leave Taken Fall 2015

Intelligent Integration of CAD and Metal Forming in Topology Optimization of Automobile Structures

Dr. Hongyan Zhang Associate Professor of MIME

College of Engineering

COLLEGE OF ENGINEERING U N I V f R S I T Y 0F TOLEDO

Office of the Dean

Mail Stop 310 Toledo, Ohio 43606-3390 419.530.8000 Phone 419.530.8006 Fax [email protected] www.eng.utokdo.edu

February 11, 2016

MEMORANDUM

TO: Professor John Barrett, JD

Interim Provost & Executive Vice President for Academic Affairs

FROM:

SUBJECT:

Nagi G. Naganathan , Ph.D., ASME Fellow <_ Professor & Dean O {· Sabbatical Leave Report from Professor Hongyan Zhang

Please find attached the sabbatical leave report from Professor Hongyan Zhang for his sabbatical leave during the 2015 fall semester.

If you require additional information, please contact me at x8000.

Cc: K. West, Sr. Director Faculty Relations/Inclusion Officer A. Afjeh, Chair, MIME Department H. Zhang, Professor, MIME Department File

http://www.eng.utokdo.edu/

Report of Sabbatical Leave Fall 2015

Hongyan Zhang Jan. 10, 2016

I spent Fall 2015 in China and Poland, as planned in my sabbatical leave proposal, and have accomplished most of the proposed objects. The details are as follows.

I. During my stay in Poland, I have prepared, with my collaborator Professor Senkara of Warsaw University of Technology, two papers on welding. One is on shunting in resistance welding. This work is basically complete, and it only needs small amount of additional experimental work for verification. Another work is on hybrid friction-ultrasonic joining process. The design has been done, and currently a visiting scholar in my lab is making a device for this process. In addition, Professor Senkara and I have worked out the complete revision of two chapters of our book, Resistance Welding: Fundamentals and Applications, for the publication of the 3rd edition of the book.

During my visit I was also invited to give a keynote speech at the 57th Polish National Welding Conference (Jachranka, Poland, Oct. 19-21, 2015). My presentation was very well received and the conference organization chairman said that my presence "raised the prestige of the conference". I also served as a session chairman at the conference. I have made extensive interaction with my Polish colleagues during my stay and a number of collaborations have been planned .

2. During my stay in China I have mainly worked on the translation of my book Resistance Welding: Fundamentals and Applications (CRC 2°d 2012) into Chinese, and on converting the results of topology optimization into CAD drawings of stamped sheet metal components. The first draft of translation has been finished, and I am working on proof-reading and revision. It is expected to be published in Nov. 2016. On the sheet metal optimization project, I and my colleagues in China have finished the development of the general rules, and have tested them on the development of a rear axle. The details are being fine- tuned, with the help of a visiting scholar from China currently working in my research lab at UT.

In summary, I have basically finished all the planned tasks during this sabbatical leave. I'm very appreciative of my department chair and the University for providing me this opportunity, at a time when we are experiencing a serious shortage of manpower. Let me know if you have any questions.

Respectfully submitted,

,'

Associate Professor Dept. of MIME, College of Engineering The Universi ty of Toledo

The University of Toledo College of Engineering Office of the Dean . / I Date Received ,J. :!7 1i...

T

Can Shunting Be Avoided?

Using an analytical model, the effects on shunting of various welding process parameters can be understood

BY HONGYAN ZHANG

he answer is yes -shunting can be avoided. Through this process, the electric current in-

tended for making a weld is diverted by its neighboring existing welds in resistance spot welding (RSW).As the heat for the shunted weld may not be sufficient, if a welding schedule is used without considering the shunting effect, an inferior weld may be produced.

Automotive manufacturers tend to put as many welds as possible in certain areas while RSW sheet metals, but caution must be taken to ensure weld quality is not compromised by shunting.

The dynamic nature of RSW, the uncertainty in materials, and the large number of process variables make it nearly impossible to accurately simu- late the shunting process and obtain a quantitative understanding of it. For instance, the total resistance of the sheet stack-up as well as the distribution of electrical resistivity in the stack-up vary from the start of the electric current application to the end.

The surface conditions, which significantly impact the electrical resistance, and, therefore, the flow of electric current, change drastically during welding and are affected by the composition of the surface layers and mechanical fit- up of the sheets. Also, a seemingly trivial change in the surface condition may produce a huge difference in the welds made.

Most of all, these factors interact among themselves in a complex manner and the influence of such interactions, when the factors are taken as functions of time, cannot be analytically presented .As a result, research on shunting has been limited and pri- marily experimental (Refs. 1,2).

In a series of recent work (Refs. 3-5), the effects of various material and process parameters were understood through experiments. Then an analytical model was developed based on the physica1 understanding of the shunting phenomenon. Using the experimental results obtained on several types of steels, researchers derived

Models that link the factors involved in shunting, which can be used to pre- dict and control shunting in resistance welding such materials.

Modeling the Shunting Effect

The prerequis ite for controlling shunting in RSW is to understand it. Although most process factors vary with time during welding, and some of

Fig. 1 - A - Schematic of shunting welding; 8 - a simplified electric circuit of the welding and shunting paths.

1 WELDING JOURNAL / OCTOBER 2015

Rcrv

I R,m,

2

them, such as resistivity of the metals, are strong functions of time, the shunting phenomenon can and has to be modeled by considering these factors fixed.

It is natural to start the analysis by considering the flow of electric current through the electrical resistances involved in shunting. A simplified electric circuit and the flow of electric current through the circuit are shown in Fig.1.

The current is determined by the relative values of electric resistances along the paths between the two electrodes. They can be classified, according to their roles, as follows: the shunting path, including contact resistances at the electrode-sheet interfaces and bulk resistance through the shunt weld, and the welding path, con- sisting of contact resistances at the electrode-sheet interfaces and bulk resistances of the top and bottom sheets, plus the contact resistance at the faying interface where the shunted weld is to be made.

The total applied electric current, I, can be split into a welding current and a shunting current, Iw and Is, respectively. The resistances along the paths were estimated for assessing the amount of electric current and, therefore, heat diverted through the shunt-

resistance is considered in the shunting path.

• The total resistance along the welding path is comprised of two parts: bulk resistance and contact resistance. The bulk part of the resistance welding path can be derived as

RbW = f{ pbulk' d, d,, t)

The contact resistance at the faying

interface in the welding path can be approximated as

where o is the yield strength of the base mefal, and FeI«trode is the applied electrode force. The introduction of the material strength and electrode force was accomplished by considering the deflection of the metal sheets under the action of electrode squeezing. This allows for the consideration of material mechanical properties and the influence of electrode force in ana- lyzing the shunting phenomenon.

Considering the electric circuit con- sisting of the shunting and welding paths as in Fig. l, the shunting current Is can be related to the overall current in the circuit, I, as

In their work, a relation between the variables such as the shunt and shunted weld sizes, welding time, current, and electrode force, as well as the sheet thickness and strength, was created by assuming the equivalence of heat needed for making the shunted weldment, including the weld nugget and heat-affected zone, and the heat generated through joule heating along the welding path.

The total heat needed for the shunted weldment can be approximated as C/P + chttP, which equals the heat generated by resistance heating Pw<R1,w + R,w)'tW'

Here 'tw is the welding time when making the shunted weld. Equating the joule heat to that needed for making the weld produces the relationship between the shunted weld size d and the welding parameters, material properties, and premade shunt weld size.

(c1d3 +c2tti2)(d? +d)2t

(0.95t)2 +Cl'itch-0.495d 0 0.49Sd1)2

C3 (df +di)t

C5t Ci; y + C4-2--2 +C4 C7t3

di +d P. 'd«trodll (Piech o.sd0)3 = 12 w ((0.95t) +(Pitch-0.49Sdo-0,495d1 )

ing path. Although they are not constant, the relative resistances at the beginning of welding are important as the initial distribution of electrical resistance is crucial in determining the electrical current distribution and heat

2 2

From this equation, it can be seen that a relatively large resistance along

generation. The contact resistance at the elec-

trode-sheet interface is assumed identical for the weld being made and its shunt weld, so its effect can be ignored for simplicity. The resistances can be classified according to their contribu- tions to welding and shunting, along their respective paths.

• The electrical resistance to the shunting current Is in the path through the previously made weld (shunt weld) can be assumed to be dominated by bulk resistance, and can be determined analytically as a function of various process parameters.

As the original faying interface is

eliminated in the shunt weld, the contact resistance in the shunting path can be assumed to be 0, and only bulk

the shunting path reduces the value of shunting current (or shunting effect). The influence of various factors on shunting can be qualitatively understood by considering their effects on the resistances, which in tum impact the percentage of electric current diverted from the welding path.

The welding current can be expressed similarly as

Iw

Heat generated in the circuit can be expressed once the resistances are derived. However, they cannot be evalu- ated as there are many unknown values in the expressions. The key is to create a link that associates the various variables with a physical event so an equation can be established.

This equation has many constants that have to be determined through carefully planned experiments for practical use. These constants contain the influence of all variables other than those that explicitly appeared in the model, including the variables that are difficult but obtainable, such as bulk and contact resistivity, and other unknown random factors in a lump- sum manner. Although it was derived using several assumptions and simpli- fications, it outlines the fundamental relationship among the variables when welding with a shunt weld.

Once the constants are determined, it can be used to derive the dependence of factors of interest on other variables. In addition, it provides a quantitative guidance for selecting welding parameters to achieve quality welds with certain restraints on weld pitch.

OCTOBER 2015 / WELDING JOURNAL 2

2

r

---- ----

Experiments - Resistance Welding Steels

A series of experiments was conducted to determine the model's coefficients. Three types of mild steels and two dual-phase (DP) steels were select-

.!, :- -- ... _ . ..

,o - ---·-- -_:_:=-

H .:. ,o \,- .......

------ -----... . :::,, --:----- -·--:--·------- . ........""-_ .. ------- .

----- ------·-·

ed. The thickness, mechanical strength, and nominal chemical composition of these commercial sheet metals are listed in Tables 1and 2.

As contact resistance might play a significant role in shunting, three

\ <---< \ \

-··--,- ,- .

types of surface conditions were created in their study: bare steel surface,

Fig. 2 - Weld widths on the coupons in the order of welding sequence.

zinc-coated (hot-dipped galvanized, HDG) surface, and a plastic film insertion (0.05-mm-thick polyvinyl chlo- ride film) used with bare or coated surfaces, representing the normal surface conditions and extremely low or high resistive surface conditions.

The plastic insertion was only used when making the shunted welds, not the shunt welds, to explore the effect of contact resistance on shunting.

Welds were made on 30 x 155 mm coupons with preselected weld pitches of 8, 15, and 25 mm. Shunted (or test) welds were made using the same schedule as the first {shunt) weld on each specimen with fixed spacing. Fixed weld pitches were used in the experiment for convenience.

The welding schedules were select- ed to make ideal-size shunt welds for the respective sheets based on experience and trials. The difference in size

other characteristics of the welds. The welding schedules and weld

pitches for welding the sheets shown in Table 1are listed in Table 3.

Truncated flat-face Cu-Cr-Zr electrodes with a 5-mm tip diameter were used for welding the steel sheets. The electrodes were also conditioned before being used in the experiments.

Experimental Observations

Effect on Weld Size

There is clearly an effect of shunting in the welds made using the aforementioned welding parameters and

Table 1 - Materials Used in the Experiment

sheet material/surface combinations and weld spacing. The weld size changes along the welding directions, and the weld sizes measured through longitudinal sections are summarized in Fig. 2.

In all three groups of specimens with different pitches, there is a drop in weld size in the first shunted welds compared with their respective shunt welds, and subsequent shunted welds tend to recover from the shunting effect with an increasing size. The con- cave downward trend is observed in all but a few cases in these groups, with the second shunted welds generally larger than the first shunted ones.

On the weld coupons with 8-mm pitches, the shunted welds continue to

between the shunt weld and shunted ones on the same coupon was meas-

Material Sheet Thickness Cmm) Coating Yield Strength CMPa)

Mild Steel 1.0 Bare 205

Table 2 - Nominal Chemical Composition Cwt-%) of the Test Materials

Material

Si

C

Mn s p

Cr

Mo Al V Fe

Mild Steel

0.01

0.07

0.26

0.012

0.014

Bal. OP590* 0.44 0.12 1.8 0.006 0.021 0.26 Bal. OP780CRef. 7) 0.23 0.1 2.33 0.03 0.02 0.04 0.06 Bal.

Table 3 -Welding Schedules and Weld Pitches

Material Current CkA) Time Cms) Force CkN) Weld Pitch (mm) 1.0-mm Mild Steel

6.0

200

1.8, 2.8

8.0, 15.0, 25.0

1.5-mm Mild Steel 6.0 400,500 1.8, 2.8 8.0. 15.0, 25.0 2.0-mm Mild Steel 6.0 500 1.8, 2.8 8.0 1.2-mm OP590 8.0 500 3.5, 5.0 8.0, 15.0, 25.0 1.25-mm DP780 8.0 500 3.0, 3.5, 4.3, 5.0 8.0. 15.0, 25.0

ured to understand the shunting ef- Mild Steel 1.5 Bare 205 fect. The welded coupons were sec- Mild Steel 2.0 Bare 205 tioned along their longitudinal direc- OP590 1.2 HOG 590

tions to obtain the dimensions and OP780 1.25 HOG 780


7

Fig. 3 - Typical welded specimens of 2.0-mm MS bare steel with an 8-mm weld pitch. A - Metallographic sections of the welds; B - indentations of the welds of the same specimen as in A The welding sequence isfrom left to right.

The use of plastic inserts at the faying interfaces when making shunted welds appears to amplify the difference in burn marks.

When welding zinc-coated steels, the welds have very similar weld marks, even for the 8-mm pitch weld coupons, as the zinc coating prevents the formation of burn marks. There- fore, it is important to recognize that in the case of multiple welding, it may be misleading to judge the weld quality by visual inspection of the weld indentation alone.

Determination of Model Coefficients and Results

Using the findings obtained in the aforementioned experiments on steel sheets, the constants c1 c2, c3 c4, c5 c5

, , , , grow in size in the welding sequence, and the growth rate is slower when the pitch is increased to 15 and 25 mm. The increase in the shunted weld size is the result of a reduced shunting effect imposed by the shunt welds, the first weld on a coupon or the prece- dent shunted welds, onto the ones made afterward.

The figure also shows that a larger drop in weld size from the shunt weld to the shunted ones happens when a plastic film was inserted into the faying interface where the shunted welds were made, compared with welding the same materials under identical conditions without a plastic insert.

Effect on Indentation

As can be seen from Fig. 2, there is

a significant reduction in size from the shunt to the shunted welds in specimens of all weld pitches. However, the

appearance of the welded coupons shows a different trend.

For instance, as seen in Fig. 3, the indentation mark of the first or shunt weld is the smallest in size compared to those of the shunted ones in the 8- mm pitch specimens. This contradicts the metallographic examination of the same specimen in the figure. In both cases with the original bare surface and plastic insert for this combina- tion.The first shunted welds are at least 10% smaller in width than the shunt welds for the specimens in Fig. 2. This observation of welds hav- ing large impression marks but smaller sizes has been obtained in other specimens as well.

With 8-mm pitches, the shunted welds have significantly wider and darker burn marks. The differences become less obvious as the weld pitches get larger to 15 and then 25 mm with original (bare) faying interfaces.

and c in the model can be determined, and the equation explicitly expressed. This should be done with sufficient replications and as many combinations of variables as possible.

In general, these constants are material dependent, and they are strongly affected by the surface conditions. Four models were created, reflecting the drastically different surface conditions at the faying interface for the shunted welds: bare steel surface (MS), zinc-coated (HOG) surface, bare steel (MS) + plastic insert, and zinc-coated (HOG) + plastic insert. The values of these four types of contact resistance are expected to vary drastically in addition to being unknown. Using experimental data and treating them in a lump-sum manner effectively circum- vents the difficulties in simulating the influence of such surface conditions.

The constants in the equation were determined through curve fitting using Mathematica™ (Ref. 8) for each of the four types of surface conditions.

After the coefficients were determined, the models were used to quan- tify the relations among the variables and weld pitch; the most important param eter in weld design is plotted in the figures as a function of other variables. The weld pitch needed to obtain a shunted weld of a certain size was expressed as a percentage of the shunt weld size to meet the requirements of weld quality, often in terms of weld size, in practice.

Fig. 4 - The effect of sheet thickness on weld pitchfor mild steels with d0 = 4.8 mm, I = 6 kA. cry = 205 MPa, F = 2.3 kN, and -r = 350 ms.

Effect of Sheet Thickness

Figure 4 shows that the required


t

weld pitch to achieve a certain sized shunted weld goes up with sheet thickness in accordance with experience. Also, a large weld pitch is necessary to have a shunted weld of size close to that of the shunt weld, so the minimum pitches increase with the required weld size. In general, the sheets with a plastic insert are more sensitive to sheet thickness, implying that the contact resistance along the welding path plays a decisive role in shunting.

A sizeable difference exists between those of interfaces with and without the plastic insert for thick sheets. For instance, the 3-mm sheet with a plastic insert needs a weld pitch of 45 mm, which is 12 mm larger than those without the plastic insert.

Effect of Welding Parameters

Sheet thickness had been largely the only variable studied before Zhang and his collaborators' work. The objec- tive was to avoid shunting through increasing the weld pitch only. As the models contain all the major welding parameters, it is possible to eliminate the shunting effect through selecting appropriate welding schedules, in addition to increasing weld pitches.

Figure SA shows that increasing welding time is an effective means of minimizing the effect of shunting as it puts more heat into a weld, which reduces the required weld pitch. The effect of welding time is amplified when the plastic insert is used. When the welding time is short, a large weld pitch is necessary.

With a long welding time, however, the increased contact resistance from the plastic insert actually works to the benefit of reducing weld pitch, as more heat is generated at the shunted weld vs. the case of bare steel. This explains that the minimum weld pitch for welding with a plastic insert is significantly smaller than those without a plastic

Fig. 5 - Dependence of weld pitch on thefollowing: A - Welding timefor the mild steel with d0 = 4.8 mm and F = 2.3 kN; B - electrodeforcefor the mild steel with d0 = 4.8 mm and -r = 350 ms; and C - shunt weld sizefor the mild steel with F = 2.3 kN and -r = 350 ms. Other parameters used were or = 205 MPa, I = 6 kA, and t = 1.5 mm.

Insert.. The influence of electrode force on

weld pitch is similar to that of welding time. A large electrode force reduces the contact resistance in the welding path and, therefore, small weld pitches are allowed with large electrode forces.

Figure SB also shows that the electrode force has a smaller effect when the plastic insert was used at the faying interface. A possible explanation is that under a large electrode force, a certain amount of (molten) plastic is


"sealed" by the electrode force exerted at the faying interface. As a result, the contact resistance is largely determined by the "entrapped" polymer, and the electrode force, which is the dominant factor on steels without a plastic insert, is less effective in creat- ing an intimate contact between the two sheets.

With the existence of plastic film at the interface, the electrode force has a lesser effect compared with that of a bare interface.

Effect of Shunt Weld Size

Figure SC shows the dependence of weld pitch on the shunt weld size as a function of achieving a certain sized shunted weld. The weld pitch needed increases rapidly with the shunt weld size. This shows that the edge-to-edge distance between the shunt and shunted welds along their centers is more important in shunting than the center- to-center distance. This observation should be incorporated in weld design.

t

w

0

0

Fig. 6 - Weld pitch as afunctian of sheet thickness. The shunted weld is assumed to have

8. There is a strong interaction between material parameters and weld· ing process variables during shunting, and shunting can be controlled through a systematic consideration of these factors.

The researchers' approach (Refs. 3-5) effectively considers the under· lined physical processes of shunting, yet avoids the difficulties involved in modeling a complex and dynamic process such as resistance welding. The modeling uncertainties and inac- curacies can be somehow absorbed by lump-summing the constants in the model. The models, with experimen- tally determined constants, have shown reasonable results that can be directly applied in welding design. i!l1J References

on equal size to the shunt weld. Far the MS, d = 4.8 mm. o = 205 MPa, and the welding

parameters are I = 6 k.A, = 350 ms, and F = 2.3 kN. For th hot·dipped DP steels, d = 5.9 1. Howe, P. 1994. Spot weld spacing

mm, or = 665 MPa, and the welding parameters are I = 8 kA.. = 500 ms, and F = 4.0 kN. effect on weld button size. SMWC VI, Paper C03.

Weld Pitc h Prediction

The weld pitches needed to create shunted welds of the same size as their shunt ones are plotted for both MS and zinc-coated DP steels in Fig. 6.

For ease of use in practice, step functions were created. The weld pitch required for welding the MS steel is larger than that for the DP steel, largely due to the difference in the surface conditions between the steels. As the contact resistance determines the proportion of the shunting current, a fay· ing interface covered by pure zinc, as in the case of DP steels, has significantly lower electrical resistance than that of a bare steel, as in MS steels.

Consequently, the proportion of shunted current is lower in the coated steels than in the bare steels, and the weld pitch required to avoid shunting in the coated steels is smaller than in the bare steels. This effect is offset slightly by the yield strength of the DP steels, as a higher strength steel tends to require a larger weld pitch because it takes more electrode force to create an intimate contact at the faying interface.

Summary

The effects on shunting of various process parameters such as material properties , surface conditions, and welding parameters can be understood using an analytical model derived through an approximation of the

physical processes during shunting with the model coefficients experi- mentally determ ined.

Models were developed on several typical MS and DP steel sheets, and the findings are summarized as fol· lows.

1. Weld pitch is the most influential factor in weld shunting, and increasing weld pitch is the most effective means of avoiding shunting.

2. Contact resistance has a signifi· cant effect on shunting. In general, large contact resistance, created by highly resistive surface conditions or low electrode forces promotes shunt· ing, and zinc coated surfaces generally behave significantly differently than bare steels.

3. A sheet of high yield strength requires a large weld pitch because of its high resistance to deformation under an electrode force.

4. Increasing welding time is effective in reducing weld pitch, as long welding generates more heat to the shunted weld.

5. The electrode force reduces the weld pitch required in general, and it is affected by other factors such as the surface condition.

6. Shunted welds may have larger/ darker electrode impressions than their respective shunt welds, even though the welds may be smaller.

7. The size of the shunt weld direct· ly affects shunting, as it dictates the length of the shunting path.

2. Zhang, H., and Senkara, J. 2012. Resistan ce Welding: Fundamentals and Applications. CRC Press/Taylor & Fran- cis Group, 2nd ed.

3. Wang, B., Lou, M., Shen, Q., Li, Y. B., and Zhang, H. 2013. Shunting ef· feet in resistance spot welding steels - Part I: Experimental study. Welding Journal 92(6): 178-s to 185-s.

4. Li, Y. B., Wang, 8., Shen, Q., Lou, M., and Zhang, H. 2013. Shunting effect in resistance spot welding steels - Part II: Theoretical analysis. Welding Journal 92(8):231-s to 238-s.

5. Li, Y. B., Wang, B., and Zhang, H. 2014. Shunting in resistance spot welding steels. 16th Sheet Metal Weld- ing Conferenc e, Livonia, Mich.

6. Rong, Y. 2012. Characterization of Microstructure s by Analytical Electron Microscopy (AEM). Higher Education Press, p. 98.

7. Alexandrov, 8., Lippold, J., Tat· man, J., and Murray, G. 2009. Non- equilibrium phase transformation dia- grams in engineering alloys. Proceed· ings of the 8th International Conference on Trends in Welding Research. David, S. A., DebRoy, T., DuPont, J. N., Koseki, T., and Smartt, H . B., eds., pp. 467-476.

8. Mathematica 8, Wolfram Re- search, Inc., v. 8.0.1.0, Copyright 1988-2011.

Dr. HONGYAN ZHANG is an associate pro/es· sor in the Dept. of Mechanical, Industria l, and

Manufacturing Engineering at the University of Toledo, Toledo, Ohio.

Based on a presentation at the Sheet Metal Welding Conference <SMWC) XVI, October

22-24, 2014, Livonia, Mich.


Steel-Step

Welding with Multiple Shunt Welds Jacek Senkara Warsaw University of Technology, Warsaw, PolanJ Hongyan Zhang The University of Toledo, Toledo, OH

Abstract

In practice, there is often more than one shunt weld existing around the weld to be made. Therefore, it is necessary to consider welding with multiple shunt welds. In this article, an equivalent welding spacing is derived when there is more than one shunt weld. This equivalent weld spacing is then compared with the critical weld spacing obtained in a previous study, and the boundary outlining the locations of a shunted weld to avoid significant shunting can be drawn. Experiments were conducted to prove the models of shunting with multiple shunt welds.

Introduction

In industrial applications of resistance spot welding there are usually several welds arranged next to each other in the same region of a component. This is usually by design for structural and handling purposes. Therefore, a pre-made neighboring weld(s) often exists when making a new weld. The existing welds may divert the electric current intended for the new weld, and this phenomenon is called shunting. As the applied electric current is shared by the weld to be made (the shunted weld) and the existing welds (the shunt welds), the heat generated in the shunted weld may not be sufficient for it to grow to its designated size. Shunting is difficult to avoid in practice, as multiple welds are commonly designed in a specific area for strength. It has been a concern in welding traditional low carbon steels, and it has more adverse effect on welding new advanced light-weighting materials such as zinc-coated high strength steels, aluminum alloys and magnesium alloys, because of their lower surface (in steels) or bulk electrical resistivity values (in Al or Mg alloys). It is common to choose a large value of the distance, called weld spacing or weld pitch, between the shunt and shunted welds to minimize the shunting effect. The weld spacing utilized in the sheet metal industry has been largely an experience-based estimate. Understanding and resolving the shunting issue is critical in large-scale application of advanced materials as resistance spot welding is a crucial enabling technique in adopting new materials in automotive vehicle construction. In the context of precision manufacturing, it is of practical interest to quantitatively determine the minimum weld spacing. However, the large number of factors involved in shunting make it difficult to isolate their influence, let alone to obtain a quantitative understanding of their effects. Although the shunting effect is well recognized by the resistance welding community, it has been discussed only in very few publications such as the work by Howe [l], the book by Zhang and Senkara [2], ASM Handbook on Welding [3], and more recently, the papers by Zhang et al. [4-7].

1. Shunting in Resistance Welding

Figure I. Shunting in resistance welding. The electrical current applied to the weld being made is diverted by its neighboring premade welds.

Figure 2. Shunting through the metal debris formed by expulsion.

Consequences • Reduced welding current -> inferior welds • Compromised structural integrity • Wasting resources

Influential Factors • Sheet geometry and physical properties • Contact resistances • Welding process parameters • Distance from, and sizes of neighboring welds

2. Equivalent Weld Spacing

The total resistance along a shunt path, without the contact resistances at the electrode-sheet interfaces, can be approximated as [shunting paper 2]

_ (Pitch -ad0 -/3d 1 f +(rt}2 Rhs -ChsAulk (di +d 2 )t

0 I (1) Take the case of 2-even thickness welding for example. The total resistance along a shunting path, without the contact resistances at the electrode-sheet interfaces, can be expressed by Equation 1. Consider a weld arrangement as shown in Figure 11a. There are two existing welds, Wl and W2, with a spacing between them Lo. When making a new weld nearby, these two welds act as shunt welds to the weld to be made. Assume that the new weld located at (x, y) has distances Pi and P2 from the two shunt welds, respectively. The shunting effect depends on these weld spacings, and the shunt weld sizes. It is also a strong function of the spacing between these two shunt welds, Lo. The resistances along shunt paths P1 and P2 have similar expressions as Equation 1, they are

and

(2)

where R1 (R2), P1 (P2), d1 (d2) are the resistance, weld spacing (weld pitch, the distance from the shunted weld), and shunt weld diameter of the first (second) shunt weld, respectively. The effects of these two shunt welds can be lumped and

(3)

represented by an equivalent shunt weld of a diameter of deq. and a weld spacing Peq.• The resistance along the equivalent shunting path is

R = C _(P_eq-._a_d_eq._-_f3 d_I )2 +_(rt f eq. bSPbullc ( d 2 + d 2 )t

eq. I (4)

The equivalency can be established by considering the equivalent resistance Req. to those in the electrical circuit formed by the two shunt welds, as shown in Figure 11b. R1and R2 are in parallel and therefore, the equivalent resistance Req. can be expressed as

(5)

Substitute the terms in Equation 5 with Equations 2 to 4, a relation between the individual shunting paths and the equivalent shunting path can be established as follows. The actual shunting paths and the equivalent shunting path can be related by

2

{ q. - adeq. - Pd, ) +(rt) di +di

eq. I

(6)

If there are more than two shunt welds, an equivalent shunt weld can be formed between a pair of two shunt welds using the above equation. Then this equivalent shunt weld can be used to form another equivalent shunt weld with other 'real' or equivalent shunt welds, and the number of shunt welds is reduced in the process. Eventually, only two shunt welds are left for the calculation of the ultimate equivalent shunt weld.

It is noted that Equation 6 doesn't explicitly contain the physical properties of the sheets such as the bulk resistivity, which means that the equivalent weld spacing (pitch) is a geometric quantity determined purely by the shunt welds considered. If there are more than two shunt welds, an equivalent shunt weld can be formed between any pair of two shunt welds using Equation 6. Such an equivalent shunt weld can be used in forming another equivalent shunt weld with other 'real' or equivalent shunt welds, and the number of shunt welds reduced in the procedure. Eventually, only two shunt welds are left for the calculation of the ultimate equivalent shunt weld.

Suppose that all the information about the shunt welds is available, another quantity has to be determined before Equation 6 can be used to solve for equivalent weld pitch, i.e., the equivalent shunt weld size, deq.. For simplicity, it can be approximated by the weighted shunt welds by their distances from the shunted weld:

(7)

Solving Equations 6 and 7 simultaneously, the equivalent weld pitch can be determined in welding involving multiple shunt welds. As can be seen from Equation 6, it is very difficult, if not impossible, to analytically solve for and explicitly express the equivalent weld spacing, a numerical approach must be utilized and the results graphically expressed.

2

(D (x, y) .,·' /

P2 /

Figure 3. Welding with two shunt welds.

P,..,.

R,,,.

Figure 4. The electrical circuits for the actual and equivalent shunting paths.

3. Influence of Various Factors on Equivalent Weld Spacing In the case of welding with a single shunt weld, if a shunted weld is located on or outside a circle centered at the shunt weld, the weld spacing (pitch) is at least the radius of the circle. In addition, such spacing is independent of the orientation of the line linking the shunt and shunted welds. When there are two or more shunt welds, however, it matters which orientation the shunted weld is located relative to the shunt welds, and the equivalent weld spacing is a function of such orientation. A shunted weld with a fixed value of equivalent weld spacing may be placed in multiple locations surrounding the shunt welds, and they form a loop with the shunt

welds at the central part. Such a loop with a fixed equivalent weld spacing, called an equivalent weld pitch loop or simply a loop hereafter, is no longer a circle, and an example is shown in Figure 3. It depicts the boarder of minimum equivalent weld spacings. On such a loop, the equivalent weld spacing of a shunted weld is fixed, and it is related, but not equal to the distance from the center, nor any of the shunt welds. As the orientation of the shunted weld relative to the shunt welds is also important, it is beneficial to define some special orientations for the easy of use in this article. Reference to Figure 1, x-axis can be termed as the 'horizontal', while y- axis 'vertical' directions. As the equivalent weld spacing cannot be directly obtained by measuring the distances in Figure 1, it makes more sense to consider the loops in understanding the characteristics of equivalent weld spacing, and its interaction with/ dependence on other variables.

The models developed in the preliminary study for the cases with single shunt weld can be extended to the cases of multiple shunt welds. Using the parameters a, /3, and r determined as in Ref. (shunting paper 2) in Equation 6, and assuming the equivalent shunt weld as a weighted function of individual shunt welds as in Equation 7, the influence of various variables can be understood. Such quantitative information is useful both for understanding the effects of the variables and for comparing with the critical weld pitch determined elsewhere, and taking necessary precaution to avoid producing inferior welds.

The procedure of finding the location of the shunted weld when there are multiple shunt welds is shown in Figure 11c, using the results of the 2-even thickness shunting model developed in the preliminary study. The possible locations of the shunted weld with a fixed equivalent spacing from two shunt welds are shown in the figure, together with those of the shunt welds. When the shunt welds are separated by 10 mm, the shunted welds are located on an oval shaped loop if a constant equivalent weld spacing of 20 mm is chosen. As the distance between the shunt welds increases, the trajectory of the shunted weld grows in the horizontal direction. In the vertical direction, however, it shrinks as the distance grows. When the spacing between the shunt welds is large, they behave more like individual shunt welds, and only the nearby weld (with respect to the shunted one) needs to be considered in shunting. In application, a critical weld spacing can be determined first using the models developed, depending on the properties of the shunt weld, etc., as well as the specific requirements as extensively discussed in Ref. 5. Such a critical weld spacing can then be used as the equivalent weld spacing for determining the allowable location(s) of the shunted weld, following the same procedure illustrated in this section.

The effects of variables in Equation 6 can be easily illustrated by plotting the trajectory of the equivalent shunt weld for a fixed value of equivalent weld spacing. Figure 3 shows the location of an equivalent shunt weld for two sheet thicknesses (t = 1.0, 2.0 mm), when the equivalent weld pitch is 10 and 20 mm, respectively. The two shunt welds have the same size as that of electrode indentation mark (d 1= d2 = di = 5.0 mm). They are separated with a distance of 10 mm. The trajectories of the equivalent shunt weld is symmetric about the origin, and they are oval shaped when

•

the equivalent shunt weld is located close to the shunt welds. Along the line between the two welds (x = 0), the distance of the equivalent shunt weld from the origin (the center of the two shunt welds) is slightly larger than the chosen equ ivalent weld pitch, and the difference gets larger as the chosen equ i valent weld pitch goes u p. Similar observations can be made along the line connecti ng the two welds, y = 0. As the equivalent shunt weld moves away from the two shunt welds, these two welds act more like one, but larger shun t weld, and a la rger spacing is required. Therefore, even wh en the two sh u nt welds are in line with the shunted weld, the effect of th e shu nt weld on the far side cannot be ignored. The figure also shows that the sheet thickness has little effect on the equivalent shunting.

Figure 5.

Equation 6 contains a variable d1, the electrode indentation mark size. Calculation indicates that its effect on the equivalent weld pitch is minima l and can be ignored without causing much error.

..

,' lO

10

0 0

" 0 10

10

,.

lO

-«:,1""40l•S

• \ho,c'ltt'l.:h I

0 Sll.l'C.....,\J

d01•).d01•7

dOl•S, dOlw't

Figure 6. Effect of shunt weld size.

t=2

t=2

The size of a shunt weld affects the overall resistance along the shunting path. However, only part of it, namely its edge near the shunted weld as analyzed in Ref. [welding journal 1], is directly involved in the process. When the two shunt welds are of equal size, the location of the shunted weld with a fixed equivalent welding spacing is symmetric about the center of the two shunt welds, as seen in Figure 4. When one is larger than the other, however, the trajectory shits to the side of larger shunt weld. Therefore, a larger weld spacing is needed when the shunted weld is located closer to the larger shunt weld.

When the shunted weld is located along the line of the two shunt welds, the closer one has larger effect in shunting, as seen in Figure 3. This is also evidenced in Figure 5. Consider the case when the shunt welds are separated by 10 mm. The shunted welds are located on an oval shaped loop with a constant equivalent weld spacing of 20 mm. It is fairly close to a circle of a radius 25 mm, which has a distance of 20 mm (the equivalent weld spacing). This circle is located inside the trajectory, which means two shunt welds together behave differently from a single shunt weld, or exactly, need a larger (equivalent) weld spacing than a single shunt weld. As the distance between the shunt welds increases, the trajectory of the shunted weld grows in the horizontal direction and the difference between the circle and the trajectory of constant equivalent weld spacing diminishes. In the perpendicular direction, however, the trajectory shrinks as the difference grows. As the spacing between the shunt welds grows, they behave more like individual shunt welds, and only the nearby weld needs to be considered in shunting.

( • I • \

Figure 7. The calculated location of the shunted weld with a fixed equivalent weld spaci ng to two shunt weld s.

The complex nature of Equation 6, especially the extensive interactions among the geometric variables involved are evidenced to some extent in the figures. A quantitative understanding of the dependence of equivalent weld spacing on other geometric variables is crucial to weld design.

4. Critical Equivalent Weld Spacing Determination

In practice, a critical weld spacing can be determined first using the formulas derived in Ref. 1[welding journal paper 2] depending on the properties of the shunt weld, etc., as well as the desire of the engineer/ designer, as extensively discussed in Ref. [welding journal paper 2]. Such a critical weld spacing can then be used as the equivalent weld spacing in determining the allowable location(s) of the shunted weld, following the same procedure illustrated in previous sections.

A critical weld spacing can be obtained by solving the relevant equations in Ref. [WJ paper 2], or the results on critical weld spacing in the same reference can be directly utilized. Figure 6 shows the boundaries of the allowable locations of a shunted weld. From Figure 4 of Ref. [WJ paper 2] a curve of interest is chosen. For instance, consider the case when the shunted weld is at least 85% of its shunt weld in size, the curve in the middle of Figure 4 in the reference can be used. For every thickness t, a corresponding critical weld spacing can be obtained from the figure. This can be used in Equation 6 as the equivalent weld spacing, with other factors fixed, to solve for the trajectory of the shunt weld. The results are shown in Figure 6. In the figure, Lo = 10 mm, d1 = 5.0 mm, d1 = d2 = 5.0 mm. The welding parameters were fixed at electric current = 6 kA, electrode force = 2.3 kN, and welding time = 350 ms for a bare low carbon steel with yield strength of 205 MPa. The locations of the shunt welds for the thicknesses form a surface as seen in the figure. In the figure there are two other surfaces for the cases of shunted weld sizes equal to 70% and 100% respectively, of their respective shunt welds'. The surfaces are of funnel shape, with the allowable shunted welds located near the shunt welds for thin sheets, and move away from them when the sheets get thicker. The differences among the locations of the shunted welds for the three cases with different expectations in shunted weld size, i.e., whether it is 70% or 85%, or even the same (100%) size as the (equivalent) shunt weld, are also strong functions of sheet thickness. Along the y-axis in the coordinates in Figure 1, the difference in the distances of the shunted weld from the center of the two shunt welds is 10mm, 11mm, and 12 mm for 0.5-mm sheets, and 40mm, 49 mm, and 60mm for 3.0-mm sheets. This equals about 10% increase for 0.5-mm sheets, and 20% for 3.0-mm ones.

.,....

Figure 8.

550

<so

I l l i

lSO

350

\

oas 10()

150 JS

10 15

JO

Figure 9. Drsunre .,(mrnJ •s

The influence of welding parameters can also be analyzed in the case of multiple shunting. For a 1.5-mm low carbon steel sheet, the required welding time to make a certain sized shunted weld at a distance from the center of the two shunt welds along y-axis as in Figure 1is shown in Figure 7. In this case, the welding current is set at 6 kA, and electrode force at 2.3 kN. In the figure the required welding time drops quickly when the distance from the shunt welds goes up. The rate lowers down as the shun ted weld gets far away from the shunt welds.

3. Experimental Verification

The plots shown i n the previous section have utilized the results from Ref. [WJ paper], expressing the minimum distance of a shunted weld has to have from the shunt welds to achieve certain sized welds. Experiments have been conducted to verify the predictions. A low carbon steel as specified in Table 1was used for this purpose.

Table 1. Low carbon steel sheets used in the experiment

,Material Sheet Thickness (mm) Coating Yield Strength (MPa) Mild Steel Mild Steel Mild Steel Mild Steel

1.0 1.5 2.0 G.O

Bare Bare Bare Bare

Q05 _ 05 :205 205

Table 2. Chemical composition of the steel sheets in Table 1.

The experiment design. All the following are done on sheets with two shunt welds of 5 mm in diameter existing. The distance between the shunt welds, center to center, is 10 mm. With such small distance (5 mm between the edges of the shunt welds), it requires extreme care when making the second shunt weld. Trials have to be made, with the predictions from Ref. [WJ paper] for the necessary welding parameters needed to make a certain sized shunted weld for the case of single shunt weld.

Part 1. With electric current = 6 kA, electrode force = 2.3 kN, and welding time = 350 ms, the following shunted weld. The shun t weld is located at (x,y) as in the following table.

Thickness (mm) 3.0

(x, y) (0,60)

Replication "

3.0 (46,46) " 3.0 (72,0) 3 2.0 (0,39) ,..,

.)

2.0 (33,33) ,., .)

2.0 (5 1,0)

.)

...,

.) ..., .) ..., .)

hickness (mm) (x, y) Replication 3.0 (0,49) ...,

3.0 (40,40) 3

3.0 (61,0) 3

(46,0) ..., .)

1.0 (0, 18) 3 1.0 ( 18,18) ...,

.) 1.0 (33,0) ...,

.)

Thickness (mm) (x, y) Replication

3.0 (0,40) 3 3.0 (34,34) ,..,

.)

3.0 (53,0) ,.., .)

2.0 (0,28) ,.., .)

2.0 (25,25) 2.0 (42,0) ,..,

.)

1.0 (0, 16) ..., .)

1.0 ( 17,17) 1.0 (31 ,0)

Part 2. With electric current = 6 kA, electrode force = 2.3 kN, and 1.5-mm sheets. The shunt weld is located at (O,y) as in Figure 1.

Replication

3

..., .)

.)

Notes:

1.0 (0,20) 1.0 (20,20) 1.0 (35,0)

Welding Time (ms) (x, y) 200 (0,28) 200 (0,33) 200 (0,40) 350 (0,22) 350 (0,25) 350 (0,29) 500 (0,20) 500 (0,22) 500 ( 0,25)

d

1. The ideal material is that shown in the table. However, if it is difficult to find such, similar materials can be used. Pay attention to the yield strength.

2. Try to be as accurate as possible. However, it doesn't have to be exact. As accurate information as possible should be recorded for the geometric measurement as well as welding para meters-not the set values, but actual readings.

3. Ideally, all the welds should be cross-sectioned and weld width measu red through standard metallographic techniques. However, i f confident enough, welds can be pulled and the button diameter measured. In shunting study, this might be difficult as the welds are located very close to each other. Even metallographic technique is used in measuring the weld width, it is not necessary to make perfect specimens. Will decide later which ones will be presented in the pa per.

4. Suggest to test/measure one specimens out of three first, and if needed, continue on the second, third.

Summary

I n addition, the distance between the shunt welds has larger effect on the surfaces when the sheets are thin, compared with the cases with thicker sheets. Similar to the cases with a single shunt weld, for any thickness a large shunted weld can be Created when i t is made sufficiently far from the shunt welds.

References

1. Howe, P., Spot weld spacing effect on weld button size, SMWC VI, Paper C03, 1994.

2. Zhang, H. and Senkara, J.: Resistance Welding: Fundan1entals and Applications. CRC Press/Taylor & Francis Group, 211

edition, Boca Raton, London, New York.

2012.

3. Tumuluru, M. D., Zhang, H., and Matteson, R.: Procedure Development and Practice Considerations for Resistance Welding, ASM Handbook (Volume 6) on Welding, ASM International Materials Park, Ohio, published Nov. 2011.

4. Wang, B., Lou, M., Shen, Q., Li, Y.B., and Zhang, H., 2013: Shunting Effect in Resistance Spot Welding Steels -Part I: Experimental Study, Welding Journal, Vol. 92, June 2013. 178-s to 185-s.

5. Li, Y.B., Wang, B., Shen, Q., Lou, M., and Zhang, H., 2013: Shunting Effect in Resistance Spot Welding Steels -Part II: Theoretical Analysis, Welding Journal, Vol. 92, August 2013. 231 -s to 238-s.

6. Li, Y.B., Wang, B., and Zhang, H., Shunting in Resistance Spot Welding Steels, 16111 Sheet Metal Weldi ng Conference, Oct. 2014, Livonia, MI.

7. Zhang, H., 2015: Can Shunting Be Avoided, Welding Journal, Vol. 94, Oct.2015. pp. 48 to 53.

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compos i t ion, dec isi vcl y a rrect t he t ype, size, and or i enta t i on of t he crys ta l s formPd . Dur ing sol id i f i ca t i on of a l i qu i d nugget , a change i n al lo· composi t i o:i takes place i n t he crvstal s bei ng preci pi ta ted, compared t o t he original compos i t i on of the a l loy. I n t he case of a very rapi d cool i ng of a spot wel dmen t, t he insuf f icien t d i f fusi on i n t he preci pi la ted sol i d cryst a l s and t he rema i n i ng l i qu i d, and the

w, rr m Af F¥tt .+nt fQ r:T.111t'8:tS' M1ti&i.N.Fri , il'J{)1i:lll: Fi&: :. 1KllA'%!i' i5?.!.lo fl:l 9 1 1El Al - Cu, A l - lg

#I t\1 \lg - Si #:, W-.& l!!:f.t !mi: H rp fi<Jfifit#l a1#. rn f islffl#Jffl iff m . M *# 1s1u #ff•, ft7 M ..f .«* \lt;c.AU rn'. tu:_N,'i tr-J.lt!rt, n ,\J, w , 1Kff tr-:u:s

mfi Af 1 •1s1 m. m1K *#h Fri- OO*· Isl#

d i f ferC'ncc i n solubi I i t y of certa in z.fn] A' :5&ti-tJlf!ix5illf.!L Jlt}K# M!.JwJf E el emrn t s i n sol i d and I i qu i cl, produce a f.EM-Fl1-ti¥ i5?.1-" fl.Ii lJl/i Jf , -.frj• Jf:3 't fiJ,'r Zfl sharp grad i en t i n the composition H1rHJl1'tH1, ¥.i -fil1./€{..Eff.\8:)J ftm1-". Fri cli s t ri bu t i on through m i c roscgregat ion. The di fference in composi t i on bet ween the fl;). D tls!:*=f-lHrli!ill01k,tJ;Hllt'i\* ZJJ& , r:> core and ou t er la·er of a cryst al i ncreases .i:Pi:.t.f¥ tf!Ef!.f& ti llihwJW-fi5{;dilil>n.LLhi:frJl@)J wi t h increasi ng d i stance bet ween t he fj(Jf'1=.. 12ilJ!t, ..ti£a1t!i:i.t ITEf!.llRJ'f-cp l iqu i clus and sol idus l ines i n a phase .tf:..f1!' £. -!'tiijlJ_!fi, ftlilH:.ff:lDTi'iE it d iagram, and decreases w i t h increasi ng 'E, fH!J,i/::i: .Ni,';{tlUS1m:5:&1=. f,t , fi!iW: d i f f us i on ra te and t he t i me span for iiJfi PlJl iijjgj tel-ri{f1./i::,F fi,J. i91j I] , W*Ji sol

i cl i i'i cat ion. I n acid i t ion to 1 Ut,J¥f U·t fiwTi'iE2it t:.Ll; f,tfl3t , Mmir"1:.bt mi

crosPgregat i on, wh i ch occurs i n the MHHt , [1!]Ht7frix: ':;W :!i fi!iflJ. sca le of crystals, segrega t i on also takes placC' as tne sol i d - 1i qu i d interface

aclvancC's in to 1hc 1i qu id, as

sol i d i f i cc1t i on proceeds, rn1d resu l ts in enr i chmen t in concen tra t i on in the rema i n i ng mel t of a l loy i ng elements. Some of t he el emen ts form etn ec t i cs of lower 1ael t i ng t emperature t ha t exi st in the l iqu i d sta t e, ma i n ly around t he cent ra l por t i on o f a nugge t af ter i t i s cooled Lo a t emp('ra ture bel ow t he sol i dus of the a l J oy but above the eu tec t i c temperature. Exampl es of such eu t ect i cs are Al - Cu, Al - \lg, and A 1 - lg - Si in alumi num al lo·s, and cert a i n compounds such as sul fur and phosphorous eu tect i cs i n steels. Because of t he i r l ower mel t ing t emperatu res, they are t he last bi ts of l i qu i d t o sol id i f y, ma i n l y a t grain boundar i es, as they arc ,ejec t ed f rom the sol i d i f i ed crystals clue to reduced solub i l i 1 · du r ing cool ing. Gra ins surrounded by such I i qu i d at the

3

boundar i es can bP t orn apart as t he l i qu i d has no sLreng t h when t hey are stretched ,

4

ei ther by ex terna l load i ng or therma l stresses i n the same way as in the case of [usion we] d ing. However, such cracking rarel v occurs i n RSW as i t. may be su ppre ssed by t he pressure f rom t h<' el ec t rodes duri ng cool i ng i f proper e lect rodes and welding schedu le are used . Af t er sol i di f icat ion, so1 id-phase trans fonna t i on may occur and i t may al ter the morphol og· of a wel d ' s m icros t ructure , wh i ch ma, be drast ical ly d i fferent from t he jus t sol id i f i ed structure. For inst ance, martensi t ic t ransformat ion may occur i n certa in steel welds wh i ch may resu l t i n a sign i f i can t ly more complex struc t u r<' than the au sten i te sol i d i f i ed from t he l iqu id .

The forma t ion of var i ous crystals, such as

dendr i t es, globu lar, and cel lu lar

crystals, i s con t ro l led by t he composit ion

and hea t transfer t hrough t he l iqu id - sol id in t er f ace. So l id i f i ca t ion occurs when t h e l i qu i d nugget reaches the l iqu idu s t emperatu re o f t he al I oy and t here i s a net hea t loss in t he 1 iqu i d: t ha t i s, t he heat d i ssipat ed from t he l i qu id i s grea t er than t ha t into t he l iqu i d. Under proper weld ing condi t ions, the wa t er cool ed electrodes may act as a large hea t si nk dur ing weldi ng. The paren t shee t met a l al so absorbs heat f rom the per i phery of t he l i qu id nugget. A possible scenario of sol id i f ica t ion dur i ng

l±I*# CW . - #> %. u!u W-mi fl [;j!, 71,fO ffi1t !r-t rt;1J fl''.lo

§ w m ffi m H 7. mm . #

1&tf.\hlA T- flkJt IJ& lJ':;c fl 1f.\iJL • ,, 7](itrrt''.} 1t!.-l'&,ti; .r1J 1i;J. -t---t-A l-& tf.1@ rr'.JW ffl o friJ IIJ . •ilfl5}1:!\ 1.l:illl.ct WJ W tt J.'tl :ill r1iJ IJJ tt M No WmMM * ,fOmhlt $&Wtl 7M M-f- Wm w Utl Mo WW•- -f-fu T- •l*IS1tili:P\l; 1;,J rg Cllea t-Affected Zone, HAZ )

7.fffl U - Q [K i*J o ill -$ rt tt A , *A AB fil ti:f ;tff r.Q , fciJ tt-j !nl -$W: W mi t qi ,i:,,,rp

o ##m M ttillH®M RSW can be cons t rnct eel based on 11'1Jt , ;tli\,!- '11,C,,;'[jl7}(t''.}ilJ i'&i'M! [;j!,filFnM11il understan d i ng L he me t a llu rgi cal and fj:Jf 1)G iJ;!f!IJ &/1t.!Lo (£.1lt.i1 $rJ* iJ lif'-fo.:! t hermal changes t ha t may occur in weld i ng. ti(9_x.-fUlnJ , y)1J ·/jf;7},(lj-f-QFniM:r?il :.tLt}t,t:,,f(jl Sol id gra i ns i n t he part iall y mol t en or fao 'W- t fl''.Jiik i rat[J mAf!LJ:)lHk:T-:1¥ mushy zone a t t he nugget - HA Z m.I E;vi[.f:31.fl]Jt 't:;.HJJ: ftj: j;' lljoJ o 00 1. 1 !fi (hea t aff ec t eel zone) borders may serve as 5F 7 - 1-,!ti its :&: 21!t tM C Transformat i on

nuclei for cryst a l grow th, and Induced Pl ast ici t y , TR IP ) W.so .is:1-iA sol i d i f ica t :on star t s 111 th i s region. J'.f,:l,1Jilitl:l *rt' ;i;!.<;$:i,'tBtfimjRfj1ifiJ±t!i.,lfil5F71f.\ J; llj;,J Further cool ing rPsu l t s i n columna r grains IB: CHi\Z) ft''.J fiflHrIffir-J #tH1J. i n d irect ions approx imat ely normal to the

*

* .

f usi on l i n0, and the sol i d - liqu i d ffil 1. 1 --1'- 780 1Pa TRIP Wl!¥J;l:';l. lH8]

i n t erface advances t oward the cen ter of the nugget. The rema ini ng rnol t en met al in t he central por L i on of the nugget sol idi f i es l as t and f orms equ iaxed grai ns when t he l iqu id vol ume i s smal l af t er much of i t s surround ing i s sol id i f i ed. Shrinkage cracks or voi ds, i f crea t ed, tend to be located i n t he nugget cen t er t ha t i s las t sol i d if ied. The actual struct ures formed in a weld nugget depend strongb·on 11eld i ng schedu l es and other cond i t ions. A careful ly crea t ed spot weld on a TR IP (Transfonna t ion Induced Plas t i c i t y) steel is shown i n P i gure 1. 1, w i t h a clear ly def ined HAZ and columnar st ructure i n t he we 1cl nugget .

FIGURE I. l A spot we l d made on 780-MPa TR IP

steel. 8

Equal ly spaced whi te dot s are indentat ion marks formed dur i ng mi crohardness t est ing. Dur ing sol i d i f i ca t ion of t he l ast bit of l i qu i d, usual l y at a loca t i on close to t he or i ginal fay i ng surface of the sheets, a def ici t of vo l ume can easi ly create cracks or voids. f n general , a vol ume def i ci t of l i qu i d met al dur i ng sol id i f ica t ion may resu l t from i nsu ff ic ien t pressure exerted on t o the weldmen t, i nsuff i c i en t mol ten me tal volume, and excessive cool i ng ra te. A large e l ec t rod e force can eff ect i vel y compensat e t he volume shr i nkage of a weldmen t dur i ng cool i ng, and can suppress t he forma t i on of voi ds or cracks.

Insuf f ic i en t heat i ng, such as that generat ed bv l ow we l d i ng current and/or short wel d i ng t i me, can resu l t in a smal l vol ume of mol 1en metal and a high cool i ng ra t e. Linder a sma ll el ec t rode force, such i nsuff ici en t mrl l i ng can eas i I y form voi els and cracks. One such exampl e i s shown in Figure 1. 2, where t he f rac1 ure surface of

00 1. 1 i:p A Ne Fl 2,.'HE,'fil !l f!Jl! f.!!'. i,: ] i:p ff !ix lliM .M ill ilitiM M m*® · # £W ttR.

- **· tli:p M #m •rr #J::.M mffin :f . eya M

. &u *wm nxM. AM m JI )J µJ %;1 j:{ f'I=.tr 'rt tn .clH!. rlI fr # fn . Mffi R tt M . *MW

mtfD/,1H1m.(I' i-'fttt faJ SI JJatf.\:f , ilTHE f.Hx +1¥J :ti'f "1!!! #m:f!l bU.1r.JJ R!J tn &.tr #M&. *- mffin . ll! Jf Jixf Ur,;JlO tt . -,15, iJJ tJi.iHt'

±ll!.MOO 1. 2 -Ctl-l .--t-.'<?. Ji\.J nfl-titJ g VI-fin # M1:: WT [IDJ::. IiJ J ir'f B!Jr ±t!!{;· +ITT - M* MR .ill

iis: -t- Et1GFnit/: 1¥J ii# Hi f& AA Af L ir,;J 1flHu IE , 11JIJ X f 1J ·t::J't0«fili 1t tP Clt/:[lij ) ,d:@i:pm

Rtr .Ufii:p kffl tl i. 00 1. 2 ( C ) rp , ffi$ i5/,.J #(lifc f/J

(tJ, -f L ifi,J J2J. !fl. Hili J't<J Jf o iJJ fit:ff: ct, tfl f!lX n (I . 1. 2 C d ) r!•(l' f'=l-l'OC,'fil T'i,·;ttMtta'"li , *WwJ *d•tt ti wm. &

i-'i1 1-tff.fr t1%F!Jlii.

5

a welclmen t fai led in i n terfaci a l frac ture

mode, reveal i ng a macroscal e shr i nkage 00 1. 2 DP600 tf·W-1 df'J WITfilfr :tH!fit'!''.lvfOSl'.ta voi d w i t h a clear evi dence of freel y f/J 9

sol i d i f i ed su r face. 9 The dendr i t es observed on t he sur face of the large vo i d

consumed the last 1iqu i cl dur ing cool i ng and

rema i nee! i n tact . The opening in Figure 1. 2c

near t he border of the void w i t h i t s surround

ing coul d resu lt from mechan i cal l oad i ng

t he cracks creat ed du e to vo l u1110 def ic i t dur

i ng sol idif icat ion of t he weld .

Tlw wh i t e box i n Figure l. 2d shows the dendr

i t es enr i ched 111 zi nc, from t he hot d i

pped z i nc coat ing of t he DP st eel. Th i s i s

an ev idence of insuf f ic i en t me! t i ng of the

nugget.

F IGLRE l. 2 l i crostructure of i n t er facial

f rac t ure surf ace i n DP600 steel weld . 9

"hen cool i ng f rom electrodes i s i mpeded , for

i ns tance, when the ac tual e lect rode - sheet

con t act area i s sma l l due to e 1ec t

rode misal ignmen t or el ectrode w0ar, mos t

of t he heat is conducted ou t ·hrough t he

sheet metal . Therefore, the las t bi t of

l i qu id sol id i f i es around t he cen t er of t he

nugge t i n t he t h ickness d irect ion . Because

of t he smal 1 \'Olume of such a 1iqu id and t he

of t en accompan i ed \'Ol ume def i ci t, cracks

and po1 si ty are of t en f ormed around the cen

t er of t he nugget a:ong t he el ectrode d i

rect ion. As these d i scon t inu i t i es are far f

rom t he HAZ a t the fay i ng i n t er faces,

t he· shou l d h,we a smal l eff ect on

st reng t h. However, such cracks very of t 0n

·opaga t e f rom t he cen ter to t he edges of

* . - mm ft W # *MITfim • .A M71'

1f.\ i1tiffi.clfitJ;JH&ft \'r- :±J g. Jlt . MFnf.fl1t «m w

,i:,-, l:1.1 T- J6: M-}Hxf4 Mi*f>!tJ,J,, jf t}' ;fl1i f,t;-fM '.k: , Ffr ijtrW ,l'fi rp'L.' it.ili:if\' ,fr $.1'JHrt1 ! ,,:; Jf r,)G tHO !§l' .. EE f- rWrp,I'., Mili .ili: fitt WITfi M

C IIAZ ) . Jlt'2if1x;j:tl¥,,8i¥.l.J:tR1 1lloJ m. . +i:t, tt'X;·1j5rttt1;;.M.W• rp ,1'., tiffi1£ w c -3 ).illW a iijGm f-!:. tfJ3l;;WlJ i:100 1. 3 pfr 1F. ,8:tl¥. :\Z91D l1:

. :tl¥,-rp0Mtf.ltt.M. m1,ffitf.l&EH , 9rlffl . r rn1

t& -f&HWilli [ t O J .

!*1 1. 3 AZ9 1D 1.1itW,8tt (fJMt , C a )

t he nugget i n t he form of branch i ng ou t. .M.:t'f...+ l:tJiHf trJ4 {1tt :i.:t IIAZ , flj1

Th i s i s d i scussed i n more deta i l i n Chapter

:i. An examp l e of sol i di f i ca t i on crack i ng a

long t he nugget t h i ckness d i rect ion i s

shown in Fi gtff e l. 3. I n weld i ng a magnesi um

allo· :\Z91D, i t was found that cracks were

formed a round the cen t er of a spot weld ,

-kITfi : (bHi'fMil! x H.ili:f1ttMM.A Jf = t o"

6

ex t end i ng from t he fay i ng su r face, across t he f usi on l i ne, to t he elect rode> sheet i n t erface. 10

FIGLRE l . 3 Morphol ogi es of cracked sect i ons of AZ9 1D wel d : (a) shr i nkage> cracks c>x t ended from nugget , through HAZ, t o surf ace: (b) a closer look a t cracks near fusion l i ne. 10

I. 2 Mc> tall urgical Characterist i cs of 1et als

The weld ing rela t c>cl metal lurgical charact

er ist ics of commonly used struc t ural ma t er ials, such as steels, aluminum alloys, and magnesi um allo·s, are presen ted i n t h is sec t ion. Copper alloys are also d i scussed si nce the\ are t he most common ma ter i a l for e lectrodes.

I. 2 Hf; WJtrt #fit * ffiWrp ffl lB MH C .ffl

;f!J )WJfrt #flt. hl ® ffl M WM . ili KilltiM .

l. 2. I Steels Proper t i es of t he paren t shrrts and t hose of the weld meta ls are det ermi ned by both t he chemical composi t i on of t he allO)'S and t he fabr ica t i on cone! i t i ons, such as heat t reatmen t and hot and cold work in The propert v map of var i ous steels, shown i n Figure 1. 4, i l lustra t es the inf luence of chemi st rv and processi ng. In genera 1, Iow carbon st ee 1s have low t ensi 1e

1. 2. 1 WJ ¥M& M0WJM1t * IB ?1 · ;f!J / Ilifi* IB.00

1. 4 , 7ft T;u,1,1r;fl:Jn(1• ftm rt:!.m:i. :t'tl rz:: 1B',M MWJfil tt. & ?1&IZUM tt WJ - ill . *• ffi M*

fllBmtt IBM . mmtt0 *&WJm miiftix +. 00 rt, rlh tt1<nJJ ®tt i::! ldl:1-t:+n!G* t

ffi ffiMffllB Mtt.. rr flR.;l:.'i!rp , M:&1:t(;l:.'f-fl];tf.l; laJ IB: 17J- i'!<Jffi 3l:fl]

strengt h and h igh duct i 1 i ty, whereas H:¥4t'tfi IBi!:.el ..R i'ifl&m RflJT°fM. 12sJ Jlt . duct i 1i t y d i mi n ishes as st rength r i ses. M{Dl,1J i§:ilfE 'fl, Mi.:l:R:!Ml-'J rn .i1;¥0.#]. The f i gure snows t ha l by a l ter i ng the 1JlliiTrh'HQ.rr-J fil&, Bi% (_ct1rtt ·l 1 1A chem i cal compos i t ion and con t rol 1 i ng phase 1':.. transformat i on s, desi rab le proper t i es of an al lov can be ach i pved. llowever, for a 00 l. 4 Jl..f'11WH·11¥J flf1f tl' fierlH] C E.l:J f-( 'f- - weld nugget and Lhe hea L-a Hc>c ted zone in WJ)t ;fff,- fl':j"J;',{Jt)

RSW, thP re i s only a 1im i t ed con t rol on t ransfonna t ions and processi ng. Therefore, t lw shee t st reng t h obta ined t hrough soph i sl i ca t eel meta 1 1 urgi ca l and mechan ical processes dur i ng f abr i ca t ion may d isappear i n a wel d metal.

7

!

8

F[GLRE 1. 4 lilechan i cal propert y d iagram of

var ious steels. (Cour lesv of Au t o-SteC'l

Part nersh i p.)

1. 2. I. l Sol i d Transformat ions i n Steels

The upper -lef t corner of t he equ i l ibrium

i ron - carbon phase d i agram i s shown i n

Fi gure l. 5 . Consi der a st eel w i t h a carbon

con Len t lower t han the eu tecto i d

composi t i on (0. 77w t. % C) coo l ed from a

tempera t u re above t he \ 3 tempera t ure, such

as i n the case of cool i ng a sol idi f i ed

nugge t or t he IIAZ. Face-cen L ered cub i c

austen i te i s t he stable phase at t h i s

tempera ture. When i t i s slow 1 ·cooled to :\3

temperat ure, t he body-cen tered cubic (BCC)

f er r i t e phase i s produced , con ta in ing a

sma 11 amount or d i ssolved carbon. The

vol ume fract ion of aust en i t e grai ns

decreases, yet t hey are progressi ve I y

enr iched in carbon. A t t he eutect o i d

temperat ure (727 ° C) , t he residual

t. 2. 1. 1 tMMq,1¥J!fj] t tfl ']Zffi ,tflffil (r-J.t:J:.f(J f;D !fil l. 5 )fir /1'0 -,HHIYi 15Q:ft1;; T-)Hfinx5t CO. 77w t. % C) A-' JIM./A jl;'j-'f A3 mH o M !fj]mt¥JW # « Mm ffl& Mo rr

iA'ri.JJ!'.Tilli {,-.:s'[Jj{<t;fl,'J C Face Cen tered

Cubic :\usten i t e , FCC) R::t.2.ffl ·t::11H t IHP ¥ A3 ilffl /J!'. , PLl:if; fwil¥J W ·l'..,.:s'L 1Jtr-J ;Jd,Hfl ( Body Cen tered Cubi c , BCC )

H ti tfi :.l:l o 14' it1i :¥u: n%ti:m5t :tiO'. i Jr OiJH,, lciJ JUwi15:fJ: nJT±fil.k o (.[ VT C 727°C )

1¥J R::#W $ft#l¥1™* -# mt¥J m # w •# c x) t¥J m ffi . h$ft - mt¥J

R::-# ffl, rr*AA TQ nx 6a. m ffi h -

t¥J mtt Mt¥Jffl , ill® R::tt mffl00 1¥J mZTillff1¥1 o mffl

austen i t e t ransforms i n to a lar.1ina t<'d x·Hx$5,: A' ;}f#tntUxli.:l!tfJi! tf.li!i eut ec t oid m i x t u re of ferr i t e and cement i t e (l,\: (r,J lli!MiJ , ffl jl;li"iZ .!VfJ1c::: r.P "=i it!Pl<R (Fe3C) , called pearl i t e. Theref ore, t he g'.[fl=;tJHR Jc , to/J ){ lj..f,'!dti*:if .hl ]J! resu l t an t steel has a structure of f err i t e l¥J M:it1'f (£ 1f;O}c "fitill.iilim. and pear l i te mi x t u re. Cemen t i t e is not a

stable : rather , i t is termed me tastable, as 1¥! l. 5 Fe - C t f*I C ilfif tl Callister, IV. D. , i

t decomposes t o i ron and graph i t e i f hel d Jr . , \1ater i a ls Sci ence and Engineer i ng : An at

an eleva ted temperat u re for a long I nt roduc t ion, 6th ed i t i on, John ll'i l ey & per i od . Same phase t ransforma t ions occur Sons, I nc. , !\ew York, 2003 . )

when cool i ng at a h i gher ra Le, bu t usual l y

a t t empera lures l ow er than t hose marked on

t he equ i l i bri wn phase di agra Al though a

m i x tu re of sof t f err i te and hard cemen t i te

i s t he t ypica l st ructure f or low-carbon

steel s, the mor phol og· of the phases i s a

strong funct i on of cool ing ra t e, and the

mix t u re can be e i ther pear l i t e or ba i ni t e

depend i ng on the cool i ng ra t e.

FIGrR E 1. 5 Fe - C phase d iagram. (Adapted

from Call i ster, W. D. , J r . , \later ia l s

Sci ence and Engi neer ing : An In t roduct ion, 6t

h ed i t i on, John W i l('' & Sons, Inc. , '>ew York, 2003. )

Isothennal phase t ransformat i on, or

somet imes ca l led t ime - t empera t ure

t ransforma t ion (TTT) d i agram, I S an

importan t too l i n und('rstand i ng t he

m i crost ruct urcs t hat may occur u pon

cool i ng. t\ TTT diagram is developed i sotherma l! · b· quenchi ng samples i n to mol ten sal t bat hs or f i xrd t emperatures and keepi ng t hem f'or predetermined prr iocls, then quench ing qu i ck l y 111 an i cr - sal t br i ne. These cl i agrams sh011 how metals transform w i t h t ime a t given tempera t ures.

Figure I. 6 i s a TTT d iagram for an i ron -

carbon alloy. A t ypi cal TTT d i agram of a pla i n carbon steel shows t he star ts and complet i ons o:·pear I i t r format i on, ba in i t e forma t i on, and mart ensi t e forma t ion. FIGL RE l. 6 A TTT d iagram for an i ron - carbon al loy or eu tec t o i cl compos i t i on : aus ten i te: B, ba i n i te : M, martensi te : P,

pea d i t e. (Adapt ed f rom Cal l i st er, II'.D.,

Jr. , Ma t er i als Sc i ence and Engi neer i ng : An In t roduct ion, 6 t h ed i t ion , John W i ley &

Sons, I nc. , :-:cw York, 2003. )

i.m ffi 00 , X. .i?J, iHli. }JL tt 31:: rt!! t] C Time - Temperat ure Transforma t ion , TTT) , .!2i:A.iQ

li™ M (fJ - I

J"J. o !JHt jl: rt!! t.JU11:1,1Jit .!2 ff r\1t Jm1f\Jr=dJc.iili A - m T M M . # ffi T

tt -JJ:'. fl{J lit fn]o Fn tt rl1d.k:ilii;;':A l!J(;j( rj 1 ,

ffi mm o . B M # Fffl jl:M• w 00 1a

rr & T jl: o ft (fJ tkfiir TTT 1 11 00 l. 6 JiJr,r;o B 7f;/c Yt . W # MH %M filo

oo 1. 6 fttfr Fix '.lH11tt irifnUttt1l:: rlht], A. # : B. JJ1 x;# : M. .f!., #: P. F,lc Yt#o

C ifh[ § Cal l ister, \\'. D. , J r . , 1a t er ial s Sci ence and Engi neet·i ng : An In t roduct i on, 6th ed i t ion, John W i l ev & Sons, Inc. , \cw York, 2003. )

equ i l i br i um cond i t i ons t ha t are rareb·met i n pract ic('. Especia l ly i n an RSW process ,

the hea t i ng and coo1 i ng rates are ex t remelv

h igh and t ransforma t i ons are far from eqt.i 1ibri um. Because most i ndustrial hea t treatmen t processes use con t rol l ed cool i ng ra t her t han i soth0rmal t ransforma t ion, con t i m1ous cool i ng t ransforma t i on (CCT) d iagrams are more representa t i Vt' of actual transformat ions t han TTT d iagrams . Cool i ng of a 11cldmen t of RSW i s also far from i sot hermal : t herefore, CCT d i agrams are mor0 appl i cab l e to u nderst and i ng t he mi crostructures of a wel dment . CCT

fix A<J o JCJt C Ef!JR:J:f\l. 91 , hn 1f.\,1<n tp if JJ!'.

r- 'itr.di. .l'l'l tt .'.&1:7.Eill 'fC1mtt{': (fJ ;id'f T o

A ftI IZ*m

mi ,r- fl!! w . rE Jlt ii u » tn ttt jl: C Cont inuous Cool i ng Transforma t i on, CCT )

tt & ffl . ffiW #M 1tt1Jigfil lr-7.E fili%- 1'1' Fillh, [;§, iir:ttt tn$ ' 1::1111tt 51:! itrn*1Wt- :J:. f l:(fJ ta :xra f J r11 %o g crT OO M (fJ ffl jl: «-

(fJ m M . TTT 00Hffe .!2 trffi!J:'.

Tfl{J tt . 't:1fl f!<rli!i,t,:JfJ:IJUr-'if' i :J.o ft

flHwitlxJ (r-J CCT 00 00 l. 7 fyjffe. El3 !!{J j;-JI. lJ fZ:t t'7lil.iiliffl'.i! t:t t'7t.P r& .4-#f O F,lc Yt i,j;(fJifiirttl: tp rHPlfilJ.ljj]l'i\i-Q>:i:/ix .IRHi:,

9

•

10

d iagrams are sim i lar to TTT d iagrams except Y-l !x:w ,tiI f!;Ix:#fiiJi:€,t; tJciUt .!;p ( TWdi w ) ±ix:# - m *m -tt#. aT M . m m**mffl

tt M . ill tt* -Fm HN' X: :tt{U ·-flj Jtt H.f-:t EX *tfi . f(jj_§.{I Jt iii!( 91 M* '&*iM$. 'f itl' IJ rtJ. IIR.:lJ;. r11f.& ,·::j 1t tn

fii:J ffl fii:JffiQ. . A ffl :@-€;- {r rti.i1rrw q:i l;lm :w:1i:rti m r1iJ . m-tff Jm t:J-m )t(:jffi k!IX1?i.Wrl:f3l rj I mfit°f='Efii:J,trl .fli&

00 1. 7 -,tg?tlfl fll:1M ft-J CCT 00 : A, !;;! !x;f,1, : F, Wdd4' : P, F),fti : B, Y-l # : \1, fli [;(; t

t ha t 1n CCT di agrams , transfonnat i ons

occur over a range of t empera tures. A

t \·pi cal CCT d iagram of a m ild steel i s shown

i n F igure l. 7. A con t i nuous cool i ng wi th a

slow cool i ng rate resu l ts i n a mi x t ure of

f err i te and pearl i t e : an intermed ia te

cool i ng t ends t o produce a mix t ure of

ferr i te, bai n i t e, and mal'lensi te: and a

rap i d cool i ng (above t he cr i ti cal cool i ng

rate) crea tes a structur e of a l l

mar tensi t e. :\!though some t echn iques such

as C'CT d i agrams take in to account t he

d ynam ic na t ure or k i net ics of phase

t ransforma t ions , t he·are usual 1:, ma ter i al

dependen t , and t here i s a ser ious l ack of

i nforma l i on on t rans rorma t i ons occurr ing

al su ch a h i gh cool i ng rate as i n RSW.

Therefore, most phase d i agrams are not

adequate whe n used 1n a quan t i ta t i ve

mann0r . i\'everthel ess, i nforma t ion of

possi ble transforma t i ons an d react i ons

dur i ng weld i ng can be ob t ained from t he

phas0 d iagrams.

FIGCRE I. 7 Typi cal CCT d i agram of a m i lei

st eel : :\, aust en i te: F, frrr i t e : P,

pea r l i te: B, ba i n i le: \1, mar tensi tc> .

L'nder certai n cond i t ions, such as when the aMm #T , -fil c •§hl) r Wt , --t -/ ·,-;':irt-Jtt t:11 --Et!.liR. tltiE t p ft-J',:t'; , tl!.if aW 1.'?: l*J 7f.3& .!c./i E.H ti'!. J.3:ftl1tf(ifilit t.11 ;;rm rms, /)(.If iHR . Ji:.Elmlli *Iffl m.trAf #F, 4-!- t1i ffii #1:.L 4 fLI;• I!!Jlt Jfi ri!Ul'.1-fr !ixr.ti fiJ < r1)i :iKi·i # ) 1ElWIH1*11'ff J1/et&i*. r.;.r; fii:J

& ill - lli*ffl &. cy ft BZ;14nl!J tt [;(;it. · )t(:iJL #.Q /:'.li fii:J

carbon (or carbon equ i valence) con ten t i s

su ff i cien tl y h i gh, a verv h i gh cool i ng

rat e, as wha t of ten occurs dur i ng l SW, may

resu l t i n mar t ens i t i c transformat i on. The

rapid cool i ng makes equ i l ibr i um phase

t rnnsforma t i ons imposs i ble, and i t tends

t o depress the t ransforma l i on

t empera t ures. A t low temperawre, t he

nu cleat ion ra t e i s h igh , whereas the grow th!Pi.i& \r- f£#1{[fii:Jtt iln\.f.9:, 1:.riJU&li!l! fii:J rate i s low. The n•su ltan t st ruct ure m.t.HrMiJ . tfi-Wltt-Jiffi1iHHJm>-.-€, ;n:.h,R 1Jf i-t (ferr i te + cemen t i t e) appears i n t he form *tim1J .fil1-tfl t't<J 1:°./iJL :iHl.t:1fJx·J ffl il&& of f i ne need l es ra t her t han th i ck l am i nar -tfl 001J r'fJ C Jfi rtH:lHBfali. Jf3;jjUm R fii:J plat es. Furt her d0pression of t he !P,0J . t.L ttL t!;, i;:;}t {E.\: l'Jr &J".Z fii:J 1? t ransf orma t ion by a h igher cool i ng ra t e may hl, JH 11.1itM:i'i\1iJ1, l.k JltYJLf!i;J r1)i:;} #f.j,:i;:

•

115

A ( E ) , 5$:t"il± ( • ) , & ( •y ) , t& lltl tfi:t'l!ii ( uts• ) {ftl**( e ) o El3rm•,

H •uuM•- .• •-

UMttffi o - , gm &ffl

: •-- UMttffi &

ffl . * n#ffl o

ffl . UM A( 5

)o . -R-mffl .-fflA 5'8

l:t"i:iJJ.:-;l. i9: j;J ;r; ( E = 210 GPa ·= 0.3 ) o

. tt n . •utt&•••uz

faJ ll!tt ( k ) 'i'fFUM -o

116

117

tin

(

m E -1

118

11

10.5

119

HAZ )

(

-

120

JI

99.

121

[-15. 0.0197] [-19.90 •2.08]ffi[9.84

YcAll*fffiA Wmax 1318 Umax 1'.19 DjaJ

UMll:J 10.22 10.23 ffl o titjJEJJI t I HAZ

R '.t' h , JlHli51Jl•y 99 Wmax 1'.19 Dia.lfil:* o

, 7 -* 8,fim!'.19 YfA£h

t h!'.19 = 0 . l ji]f

1[=.1'Dia.].$Z q:i:1il1 1'.19 Yf A:!i! HAZ R '.t'o

. ttm1[ffl r , B-@ m =

tt -ffl- , ti*fffiAft8

4'fffi flt Bil0

- 7 - •nYc•tt

fffiflffitt!'.19 7Mo -ffi r:

122

123

124

Structure Optimization on a Rear Axel

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Sabbatical Leave Taken Fall 2015 Intelligent Integration ... H-Fall 2015.pdfOn the sheet metal optimization project, I and my colleagues in China have finished the development of general