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International Journal of Fatigue 30 (2008) 90–105

JournalofFatigue

Failure modes and fatigue life estimations of spot friction weldsin lap-shear specimens of aluminum 6111-T4 sheets.

Part 2: Welds made by a flat tool

P.-C. Lin a, J. Pan b,*, T. Pan c

a Mechanical Engineering, National Chung-Cheng University, Chia-Yi 621, Taiwanb Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109, USA

c Ford Research and Advanced Engineering, Ford Motor Company, Dearborn, MI 48121, USA

Received 9 June 2006; received in revised form 17 February 2007; accepted 25 February 2007Available online 2 March 2007

Abstract

Failure modes of spot friction welds made by a flat tool in lap-shear specimens of aluminum 6111-T4 sheets are investigated based onthe approach presented in Part 1. Optical and scanning electron micrographs of the welds before and after failure under quasi-static andcyclic loading conditions are examined. The micrographs show that the microstructure, geometry, and the failure modes of the welds madeby the flat tool are quite different from those of the welds made by a concave tool. Under quasi-static loading conditions, the failure mainlystarts from cracking near the boundary of the stir zone close to the upper sheet surface inside the weld. Under cyclic loading conditions, theexperimental results indicate three types of fatigue cracks. The first type initiates and grows near the boundary of the stir zone close to theupper sheet surface inside the weld as that under quasi-static loading conditions. The second type initiates and grows into the lower sheetoutside the stir zone. The third type initiates from the bend surface of the upper sheet outside the weld. Under low-cycle loading condi-tions, the dominant kinked fatigue cracks are the first type growing near the boundary of the stir zone. Under high-cycle loading condi-tions, the dominant kinked fatigue cracks are the second type growing in the lower sheet outside the stir zone. Based on the experimentalobservations of the paths of the dominant kinked fatigue cracks, the fatigue crack growth model presented in Part 1 is then adopted toestimate the fatigue lives of the spot friction welds made by the flat tool. The fatigue life estimations based on the fatigue crack growthmodel with the global and local stress intensity factors as functions of the kink length and the experimentally determined kink angles agreewell with the experimental results. A comparison of the experimental results suggests that the failure strengths of spot friction welds underquasi-static loading condition can cautiously be used as references to select a tool and the corresponding processing parameters. However,fatigue tests must be performed to validate the performance of spot friction welds under cyclic loading conditions.� 2007 Elsevier Ltd. All rights reserved.

Keywords: Spot friction weld; Friction stir spot welding; Failure mode; Kinked crack; Fatigue crack propagation; Fatigue life; Lap-shear specimen;Aluminum 6111-T4

1. Introduction

Recently, a new spot friction welding (SFW) technologyfor joining aluminum sheets has been developed by MazdaMotor Corporation and Kawasaki Heavy Industry [1,2].The microstructures and failure modes of spot friction

0142-1123/$ - see front matter � 2007 Elsevier Ltd. All rights reserved.

doi:10.1016/j.ijfatigue.2007.02.017

* Corresponding author. Tel.: +1 734 764 9404; fax: +1 734 647 3170.E-mail address: jwo@umich.edu (J. Pan).

welds under quasi-static loading conditions have been stud-ied by many researchers based on experimental observa-tions [3–8].

As discussed in Part 1, the fatigue behaviors of spot fric-tion welds have not been investigated from the fracturemechanics viewpoint. However, past relevant researchworks on the fatigue behaviors of resistance spot weldsbased on fracture mechanics have been conducted, forexample, see Pook [9], Swellam et al. [10], Zhang [11,12],

P.-C. Lin et al. / International Journal of Fatigue 30 (2008) 90–105 91

Newman and Dowling [13], Pan and Sheppard [14], Wanget al. [15,16], Wang and Pan [17], and Lin et al. [18]. A briefreview of these relevant research works is presented in Part1.

In this part, the failure modes of aluminum 6111-T4spot friction welds made by a flat tool in lap-shear speci-mens are investigated based on the approach presented inPart 1 where the failure modes of aluminum 6111-T4 spotfriction welds made by a concave tool are presented. Notethat both types of spot friction welds made by the flat tooland the concave tool are potential candidates for mass pro-duction. Since the failure modes of the welds made by theflat tool are more complex than those made by a concavetool, a separate presentation of the failure modes and fati-gue life estimations of the welds in Part 2 appears to bewarranted. In this part, optical and scanning electronmicrographs of the welds made by the flat tool beforeand after failure under quasi-static and cyclic loading con-ditions are examined. The failure modes of the spot frictionwelds under quasi-static, low-cycle and high-cycle loadingconditions are then investigated. The dominant kinked fati-gue cracks for the spot friction welds are identified. Basedon the experimental observations of the paths of the dom-inant kinked fatigue cracks, the fatigue crack growth modelpresented in Part 1 is then adopted to estimate the fatiguelives of the spot friction welds made by the flat tool. Thefatigue life estimations based on the fatigue crack growthmodel with the experimentally determined kink angles arecompared with the experimental results for the spot frictionwelds in lap-shear specimens. A comparison of the failuremodes, failure strengths and fatigue lives of the welds madeby the flat and concave tools is then presented. Finally, theexperimental results and fatigue life estimations are dis-cussed and some conclusions are given.

2. Spot friction welds of aluminum 6111-T4 sheets

In this investigation, aluminum 6111-T4 sheets with thethickness of 0.94 mm were used. A description of the spotfriction welding process and the two different types of toolscan be found in Part 1. In this part, we concentrate on thefailure modes and the fatigue life estimations of the spotfriction welds made by a tool with a flat shoulder as shownin Fig. 1c in Part 1. Note that the failure modes and thefatigue life estimations of the spot friction welds made bya concave tool can be found in Part 1. Fig. 1 shows a crosssectional view and close-up views of a spot friction weldmade by the flat tool before testing. Fig. 1a shows an opti-cal micrograph of the cross section. As shown in the figure,the indentation profile reflects the shape of the probe pinand the flat shoulder of the tool. The plunge depth canbe estimated from the indentation profile as 1.60 mm forthis particular weld. The bottom surface is kept almost flatexcept near the central hole. Near the central hole, twogray areas represent the fine grain stir zones where theupper and lower sheets are bonded. The gray stir zoneextends out with a maximum size about 1 mm from the

central hole profile. Two notches, marked as N1 and N2,can be seen in the figure. Fig. 1b shows a close-up opticalmicrograph of region I where the notch, marked as N1,extends and becomes a crack. The location of the cracktip is marked in the figure. As shown in Fig. 1b, the inter-facial surfaces of the upper and lower sheets were distortedinto the macroscopic curved surfaces outside the stir zone.Note that the nugget diameter can be determined based onthe location of the original crack tip. The nugget diameteris estimated to be 5.88 mm. Fig. 1c shows a close-up opticalmicrograph of region II where the zig-zag curved interfa-cial surfaces, marked by two black arrows, become vagueand disappear into the stir zone. A void is shown nearthe zig-zag curved interface and the void can be consideredas a defect for the spot friction weld. The crack tip locationcan be identified by a scanning electron micrograph of thecrack tip region as shown in Fig. 1d. A detailed discussionof the metallurgical aspects of aluminum 6111-T4 spot fric-tion welds made by a flat tool can be found in Mitlin et al.[8].

As shown in Fig. 1a, the flat tool shoulder squeezed outa portion of the upper sheet material and, consequently,the thickness of the upper sheet material decreased underthe shoulder indentation. The material under the shoulderindentation flowed outward and resulted in a radial expan-sion of the upper sheet material along the outer circumfer-ence of the shoulder indentation. However, due to theconstraint of the neighboring material, the sheet was there-fore bent along the outer circumference of the shoulderindentation. In Fig. 1a, the bend is marked as B1 andB2. In contrast to the spot friction weld made by the con-cave tool investigated in Part 1, the flat tool shoulderinduced a plastic flow and stir pattern which is differentfrom that under the concave tool shoulder. Therefore, theshape and size of the stir zone of the weld made by the flattool as shown in Fig. 1a are totally different from thosemade by the concave tool as shown in Part 1. When theconcave tool was used to make the weld, more materialcould be confined and stirred under the tool during thewelding process. However, when the flat tool was used tomake the weld, material under the tool can be relativelyeasy to be squeezed out. This could be the main reason thatthe stir zone of the weld made by the flat tool is smallerthan that of the weld made by the concave tool. It shouldbe also noted that the processing conditions of the twowelds, such as the tool downward force, the rotationalspeed and the welding time, are quite different. Differentprocessing conditions can also result in different shapesand sizes of the stir zones for a given tool geometry. Asshown in Fig. 1a, the squeezed out material from the shoul-der indentation also formed a ring along the outer circum-ference of the shoulder indentation on the top surface ofthe upper sheet.

Fig. 2 shows the deformed shape of a spot friction weldmade by a flat tool based on a preliminary axisymmetricthermal–mechanical finite element modeling of spot fric-tion welding process. Near the bend, the finite element

Fig. 2. Deformed shape of a spot friction weld made by a flat tool based on a preliminary axisymmetric thermal–mechanical finite element modeling ofspot friction welding process.

Fig. 1. (a) An optical micrograph of the cross section along the symmetry plane of a spot friction weld made by the flat tool, (b) a close-up opticalmicrograph of region I, (c) a close-up optical micrograph of region II and (d) a close-up scanning electron micrograph of the crack tip region as shown in(c).

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mesh needs to be refined to avoid the large deformation ofthe coarse element as shown in Fig. 2. The details of thecomputational results will be reported elsewhere. Althoughthe finite element analysis is preliminary, the result of thefinite element computation shows that the formation ofthe bend due to the outward flow of the material underthe tool indentation is quite consistent with that shown inFig. 1a.

3. Experiments

Lap-shear specimens were made by using two25.4 mm · 101.6 mm sheets with a 25.4 mm · 25.4 mmoverlap area. Fig. 3 shows a lap-shear specimen with a spotfriction weld made by the flat tool. Comparing to the weldmade by the concave tool as shown in Fig. 4a in Part 1, theweld shown in Fig. 3 appears to be larger due to the larger

Fig. 3. A lap-shear specimen with a spot friction weld made by the flat tool.

Life

Loa

d ra

nge

(N)

103

104

105

106

400

800

1200

1600

2000

2400

Fig. 5. Experimental results for the spot friction welds made by the flattool in lap-shear specimens under cyclic loading conditions.

P.-C. Lin et al. / International Journal of Fatigue 30 (2008) 90–105 93

outer protruded ring on the surface, which comes from theflow of the material under the tool shoulder indentation asdiscussed earlier. As shown in the figure, two doublers aremade by folding two square parts of the sheets near theends (25.4 mm · 25.4 mm). Lap-shear specimens were firsttested by using an Instron 4502 testing machine. The loadand displacement were simultaneously recorded during thetesting. Fig. 4 shows a typical load–displacement curve of aspot friction weld made by the flat tool under lap-shearloading conditions. Note that the slackness in the test setuphas been removed. The average failure load of tested spec-imens is 1.94 kN. The lap-shear specimens were then testedby using an Instron servo-hydraulic fatigue testingmachine. The details of the fatigue experiments are identi-cal to those presented in Part 1 and are not repeated here.Fig. 5 shows the experimental results for the spot frictionwelds made by the flat tool in lap-shear specimens undercyclic loading conditions.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.60

0.5

1

1.5

2

2.5

Displacement (mm)

Loa

d (k

N)

Fig. 4. A typical load–displacement curve of a spot friction weld made bythe flat tool under lap-shear loading conditions.

4. Fatigue modes under quasi-static and cyclic loading

conditions

4.1. A two-dimensional general overview of failure modes

We conducted experiments under quasi-static and cyclicloading conditions. Based on the experimental observa-tions, the failed spot friction welds under quasi-static load-ing conditions show one failure mode. The failed spotfriction welds under cyclic loading conditions with the fati-gue lives from 103 to 104 show a similar failure mode. Thefailed spot friction welds under cyclic loading conditionswith the fatigue lives from 104 to 105 show another failuremode. Since the failure modes of the spot friction welds arequite complex under quasi-static and cyclic loading condi-tions, we first present a two-dimensional general overviewof the failure modes under loading conditions of quasi-sta-tic loading, low-cycle fatigue (lives of 103–104), and high-cycle fatigue (lives of 104–105).

Fig. 6a shows a schematic plot of the cross section alongthe symmetry plane of a lap-shear specimen made by theflat tool with the sheet thickness t under an applied load

t

Doubler

Doubler

Leg 1

Leg 2

Stir zone

ACD

EB

Failure mode Quasi-static A B C

Low-cycle fatigue A B CHigh-cycle fatigue D, E A B C

b

c→ →→ →

→ → →

Fig. 6. (a) A schematic plot of a lap-shear specimen made by the flat tool with the sheet thickness t under an applied force (shown as bold arrows), (b) aschematic plot of the cross section near the spot friction weld made by the flat tool and (c) the failure modes of spot friction welds made by the flat toolunder quasi-static, low-cycle and high-cycle loading conditions.

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(shown as the bold arrows). Fig. 6b shows a schematic plotof the cross section near the spot friction weld under a stat-ically equivalent combined tensile and bending load. Inthese figures, the shadow represents the stir zone, the dashline represents the unwelded interfacial surface and the thinsolid line represents either fracture surface or fatigue crack.Fig. 6c shows a table which summarizes the failure modesof spot friction welds under quasi-static, low-cycle andhigh-cycle loading conditions.

As shown in Fig. 6b and as listed in Fig. 6c, under quasi-static loading conditions, a crack (marked by A) near theupper right portion of the spot friction weld appears toemanate from the original crack tip and propagate nearthe boundary of the stir zone. Then a shear failure, markedby B, occurs at the end of the crack. The failure then prop-agates along the nugget circumference and, finally, theupper sheet is torn off with some part of the nugget,marked by C. Note that the shear failure C occurs withinthe stir zone, in contrast to the shear failure B occurringnear the boundary of the stir zone. Under low-cycle load-ing conditions, a fatigue crack (marked by A) near theupper right portion of the spot friction weld appears toemanate from the original crack tip of the spot frictionweld and propagate near the boundary of the stir zone.Then a shear failure, marked by B, occurs at the end ofthe fatigue crack. The experimental observations suggestthat the fatigue crack (marked by A) appears to be thedominant crack that propagates through the sheet thick-ness at location B. Finally the upper sheet is torn off withsome part of the nugget, marked by C. Under high-cycleloading conditions, a fatigue crack (marked by D) nearthe lower left portion of the spot friction weld appears toemanate from the original crack tip. Near the upper right

portion of the spot friction weld, another fatigue crack(marked by E) appears to emanate from the bend surface.However, the experimental observations suggest that thefatigue crack (marked by D) appears to be the dominantcrack that propagates through the sheet thickness. Thena fatigue crack (marked by A) appears to emanate fromthe original crack tip on the right side of the spot frictionweld. The fatigue crack (marked by A) then propagatesnear the boundary of the stir zone and a shear failure,marked by B, occurs at the end of the fatigue crack.Finally, the upper sheet is torn off with some part of thenugget, marked by C. In the following, we present micro-graphs to show the details of the failure modes of spot fric-tion welds in lap-shear specimens.

4.2. Failure mode under quasi-static loading conditions

Fig. 7a shows an optical micrograph of the cross sectionalong the symmetry plane of a partially failed spot frictionweld made by the flat tool under quasi-static loading con-ditions. The arrows in Fig. 7a schematically show the direc-tion of the applied load. As shown in Fig. 7a, near theupper right portion of the spot friction weld, a crack(marked as crack 2) appears to emanate from the originalcrack tip and propagate near the boundary of the stir zone.It should be noted that the location of the original crack tiphas been identified by both optical and scanning electronmicrographs as shown in Fig. 1. Then a shear failure,marked by S2, occurs at the end of crack 2. Finally, thefailure propagates along the nugget circumference andthe upper sheet is torn off at the location, marked by S1,with a small part of the nugget. Note that no failure ordamage can be seen in the lower left leg, marked as Leg 1.

Fig. 7. (a) An optical micrograph of the cross section along the symmetry plane of a partially failed spot friction weld made by the flat tool under quasi-static loading conditions, (b) a close-up scanning electron micrograph on the fracture surface of region I and (c) a close-up scanning electron micrographon the fracture surface of region II.

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Fig. 7b shows a close-up scanning electron micrographof region I on the fracture surface of crack 2 from anotherfailed specimen. Fig. 7c shows a close-up scanning electronmicrograph of region II on the fracture surface of shearfailure S2 from another failed specimen. The bold arrowsin these figures schematically show the propagation direc-tions of the macroscopic crack fronts. Fig. 7b shows smalldimples on the fracture surface of crack 2. In the region ofsmall dimples, a wavy structure inclined to the horizontaldirection can be seen. The wavy structure may come fromthe microstructure of the material near the stir zone due tothe processing conditions since similar wavy structures canbe seen on the fracture surfaces of the spot friction weldsunder low-cycle and high-cycle loading conditions as dis-cussed later. Note that the small dimples suggest that thecurved fracture surface where crack 2 grows through is wellbonded before the failure. Fig. 7c shows elongated dimpleson the fracture surface of shear failure S2.

Fig. 8. An optical micrograph of the cross section along the symmetry plane of103.

4.3. Failure mode under low-cycle loading conditions

Fig. 8 shows an optical micrograph of the cross sectionalong the symmetry plane of a failed spot friction weldmade by the flat tool at the fatigue life of nearly 103. Notethat the spot friction weld was failed and separated. Thearrows in Fig. 8 schematically show the direction of theapplied load. As shown in Fig. 8, near the upper right por-tion of the spot friction weld, a fatigue crack (marked ascrack 2) appears to emanate from the original crack tipand propagate near the boundary of the stir zone. Fatiguecrack 2 can be considered as a kinked crack emanatingfrom the original crack tip. Then a shear failure, markedby S2, occurs at the end of fatigue crack 2. The failure thenpropagates along the nugget circumference and, finally, theupper sheet is torn off at the location, marked by S1, withsome part of the nugget. A similar failure mode is observed

a failed spot friction weld made by the flat tool at the fatigue life of nearly

Fig. 9. (a) The lower sheet of a failed lap-shear specimen with a spot friction weld made by the flat tool at the fatigue life of nearly 103, (b) a top view of aspot friction weld on the lower sheet of the failed specimen, (c) a bottom view of a spot friction weld on the lower sheet of the failed specimen, (d) a topview of a spot friction weld on the upper sheet of the failed specimen and (e) a bottom view of a spot friction weld on the upper sheet of the failed specimen.

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for spot friction welds made by the flat tool in lap-shearspecimens under quasi-static loading as discussed earlier.

Fig. 9a shows the lower sheet of a failed lap-shear spec-imen with a spot friction weld made by the flat tool at thefatigue life of nearly 103. The circumferential failure modeor the nugget pull-out failure mode can be seen from thespot friction weld on the lower sheet of a failed specimenin Fig. 9a. Figs. 9b and c show a top view and a bottomview of a spot friction weld on the lower sheet of the failedspecimen, respectively. Figs. 9d and 10e shows a top viewand a bottom view of a spot friction weld on the uppersheet of the failed specimen, respectively. As shown inFigs. 9a and b, a small portion near the left side of theremaining weld nugget is sheared off due to the tearing ofthe upper sheet. The rough region surrounding the remain-ing nugget is possibly due to the contact and rubbing of theupper sheet during the welding process. As shown inFig. 9d, the protruded ring comes from the flow of the

material under the tool shoulder indentation. As shownin Fig. 9e, a surface is protruded out of the bottom surfaceof the upper sheet due to the shoulder indentation. A smallportion of the remaining nugget is attached on the left por-tion of the hole circumference, marked by an arrow.

Fig. 10a shows an optical micrograph of the cross sec-tion along the symmetry plane of a spot friction weld inthe lower sheet of a failed specimen made by the flat toolat the fatigue life of nearly 103. The upper sheet wasremoved for easy access of the surface for scanning electronmicrographs. The large bold arrow in Fig. 10a schemati-cally shows the direction of the applied load on the lowersheet. Fig. 10b shows a close-up scanning electron micro-graph of region I on the unwelded interfacial surface.Fig. 10c shows a close-up scanning electron micrographof region II on the fracture surface of fatigue crack 2.Fig. 10d shows a close-up scanning electron micrographof region III on the fracture surface between those of fati-

Fig. 10. (a) An optical micrograph of the cross section along the symmetry plane of a spot friction weld in the lower sheet of a failed specimen made by theflat tool at the fatigue life of nearly 103, (b) a scanning electron micrograph of region I, (c) a close-up scanning electron micrograph of region II, (d) a close-up scanning electron micrograph of region III and (e) a close-up scanning electron micrograph of region IV.

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gue crack 2 and shear failure S2. Fig. 10e shows a close-upscanning electron micrograph of region IV on the fracturesurface S1. Note that the scanning electron micrographs inFigs. 10b–e are obtained from another failed specimen. Thebold arrows in Figs. 10c and d schematically show thepropagation directions of the macroscopic fatigue crackfronts. In order to be consistent with the directions of thefatigue crack propagation in Fig. 10a, we rotate the scan-ning electron micrograph by 180� in Fig. 10d.

Fig. 10b shows the mark of contact and rotation on theunwelded interfacial surface. No damage or small dimplescan be seen on the surface. This indicates that theunwelded interfacial surface is not bonded. Fig. 10c showssmall dimples and wavy fracture surface of fatigue crack 2.The wavy structure shown in Fig. 10c is quite similar tothat shown in Fig. 7b for the fracture surface underquasi-static loading conditions. Fatigue striations orientedin the horizontal direction, marked by small arrows, canalso be seen on a small portion of the fracture surface.Fig. 10d shows the transition region from the surface offatigue crack 2 (lower portion) to the surface of shear fail-ure S2 (upper portion). The surface with elongated dimples

in the upper portion of the figure represents the fracturesurface of shear failure S2. The surface with dimples inthe lower portion of the figure represents the fracture sur-face of the kinked fatigue crack 2. Between the fracturesurfaces of fatigue crack 2 and shear failure S2, the surfacewith coarse fatigue striations in the middle portion of thefigure represents the transition fatigue crack surface wherethe abrupt change of the crack propagation direction takesplace. Fig. 10e shows smeared surface and some undam-aged elongated dimples on the fracture surface S1 wherethe upper sheet is torn off. As shown in the figure, mostof the dimples are smeared possibly due to rubbing andtearing of the upper sheet.

4.4. Failure mode under high-cycle loading conditions

Fig. 11a shows an optical micrograph of the cross sec-tion along the symmetry plane of a partially failed spotfriction weld made by the flat tool at the fatigue life ofnearly 105. The arrows in Fig. 11a schematically show thedirection of the applied load. Two fatigue cracks can beseen in Fig. 11a. Near the lower left portion of the spot

Fig. 11. (a) An optical micrograph of the cross section along the symmetry plane of a partially failed spot friction welds made by the flat tool at the fatiguelife of nearly 105, (b) optical micrographs of a partially failed spot friction weld cross sectioned in the directions of OB, OC, and OD, respectively. Thedirections of OB, OC, and OD are 45�, 90� and 135� with respect to the loading direction of the upper sheet, respectively.

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friction weld, a fatigue crack (marked as crack 1 0) in thelower sheet appears to emanate from the original cracktip of the spot friction weld. Near the upper right portionof the spot friction weld, another fatigue crack (markedas crack 2 0) in the upper sheet appears to emanate fromthe bend surface, marked as B2. The experimental observa-tions indicate that fatigue crack 1 0 can damage a largerangular span of the circumference of the spot friction weldthan fatigue crack 2 0. Therefore, fatigue crack 1 0 appears tobe the dominant kinked crack that emanates from the ori-ginal crack tip and propagates through the sheet thickness.As later shown in Fig. 13a from a failed spot friction weld,the micrograph shows that a fatigue crack (marked bycrack 2) appears to emanate from the original crack tipon the right side of the spot friction weld. Fatigue crack2 then propagates near the boundary of the stir zone anda shear failure, marked by S2, occurs at the end of the fati-gue crack. Finally, the upper sheet is torn off at the loca-tion, marked by S1, with some part of the nugget. Thefinal stage of the failure appears to be similar to that under

low-cycle loading conditions as shown in Fig. 8 and thatunder quasi-static loading conditions as shown in Fig. 7a.Note that micrographs of different cross sections of a failedspot friction weld made by the flat tool at the fatigue life ofnearly 105 can be seen in Fig. 11b.

Fig. 11b shows micrographs of a partially failed spotfriction weld cross sectioned in the directions of OB, OC,and OD, respectively, which are 45�, 90� and 135� withrespect to the loading direction of the upper sheet, respec-tively. The location of the material point near a spot fric-tion weld with respect to the loading direction has beendefined in Fig. 11 in Part 1. Note that some portions nearthe central hole of the spot friction weld were removed dur-ing the cross sectioning and polishing processes. In thedirection of OB, two small fatigue cracks, marked as crack2a* and crack 2b*, emanate from the bend surface, markedas B2*. In the direction of OC, a fatigue crack (marked ascrack a*) emanates from the original crack tip and propa-gates near the boundary of the stir zone. In the directionof OD, two small fatigue cracks, marked as crack 1a*

P.-C. Lin et al. / International Journal of Fatigue 30 (2008) 90–105 99

and crack 1b*, emanate from the original crack tip. Asshown in Fig. 11b, the small fatigue cracks 1a* and 1b* rep-resent the extension of fatigue crack 1 0 in Fig. 11a and thesmall fatigue cracks 2a* and 2b* represent the extension offatigue cracks 2 0 in Fig. 11a. Fatigue crack a* in the direc-tion of OC in this case grows mostly under dominant modeIII conditions and may represent the transition crack fromthe kinked cracks 1a* or 1b*.

Fig. 12a shows the lower sheet of a failed lap-shear spec-imen with a spot friction weld made by the flat tool at thefatigue life of nearly 105. The circumferential failure modeor the nugget pull-out failure mode can be seen from thespot friction weld on the lower sheet of a failed specimenin Fig. 12a. Figs. 12b and c show a top view and a bottomview of a spot friction weld on the lower sheet of the failedspecimen, respectively. Figs. 12d and e show a top view anda bottom view of a spot friction weld on the upper sheet ofthe failed specimen, respectively. As shown in Figs. 12a–c,

Fig. 12. (a) The lower sheet of a failed lap-shear specimen with a spot friction wspot friction weld on the lower sheet of the failed specimen, (c) a bottom viewview of a spot friction weld on the upper sheet of the failed specimen and (e) a bo

a fatigue crack can be seen along the left portion of thenugget circumference. Note that the fatigue crack on thelower sheet of the failed specimen corresponds to fatiguecrack 1 0 in Fig. 11a. Both Figs. 12d and e show the holein the upper sheet due to the nugget pull-out. Fig. 12eshows a small fatigue crack, marked by two arrows, alongright portion of the circumference of the shoulder indenta-tion. Note that the small fatigue crack on the upper sheetof the failed specimen corresponds to fatigue crack 2 0 inFig. 11a. As shown in Fig. 12e, a small portion of theremaining nugget is attached on the left portion of the holecircumference (the white area marked by an arrow).

Fig. 13a shows an optical micrograph of the cross sec-tion along the symmetry plane of a spot friction weld inthe lower sheet of a failed specimen made by the flat toolat the fatigue life of nearly 105. The upper sheet wasremoved for easy access of the surface for scanning elec-tron micrographs. The large bold arrow in Fig. 13a

eld made by the flat tool at the fatigue life of nearly 105, (b) a top view of aof a spot friction weld on the lower sheet of the failed specimen, (d) a topttom view of a spot friction weld on the upper sheet of the failed specimen.

Fig. 13. (a) An optical micrograph of the cross section along the symmetry plane of a spot friction weld in the lower sheet of a failed specimen made by theflat tool at the fatigue life of nearly 105, (b) a close-up scanning electron micrograph of region I, (c) a close-up scanning electron micrograph of region II,(d) a close-up scanning electron micrograph of region III and (e) a close-up scanning electron micrograph of region IV.

100 P.-C. Lin et al. / International Journal of Fatigue 30 (2008) 90–105

schematically shows the direction of the applied load onthe lower sheet. Fig. 13b shows a close-up scanning elec-tron micrograph of region I on the fracture surface of fati-gue crack 1 0. Fig. 13c shows a close-up scanning electronmicrograph of region II on the fracture surface of fatiguecrack 2. Fig. 13d shows a close-up scanning electron micro-graph of region III on the fracture surface between thoseof fatigue crack 2 and shear failure S2. Fig. 13e shows aclose-up scanning electron micrograph of region IV onthe fracture surface S1. The bold arrows in Figs. 13b–dschematically show the propagation directions of the mac-roscopic fatigue crack fronts.

Fig. 13b shows fatigue striations and cleavage steps onthe fracture surface of fatigue crack 1 0. Fig. 13c showssmall dimples and fatigue striations, marked by smallarrows, on the wavy fracture surface of fatigue crack 2.The microscopic features in Fig. 13c are very similar tothose in Fig. 10c. A wavy structure can be seen inFig. 13c as that in Fig. 10c for the fracture surface underlow-cycle loading conditions and Fig. 7b for the fracturesurface under quasi-static loading conditions. Fatigue stri-ations, marked by small arrows, can also be seen on a smallportion of the fracture surface.

Fig. 13d shows the transition region from the surfaceof fatigue crack 2 (lower portion) to the surface of shearfailure S2 (upper portion). The microscopic features inFig. 13d are very similar to those in Fig. 10d. The sur-face with elongated dimples in the upper portion of thefigure represents the fracture surface of the shear failureS2. The surface with dimples in the lower portion of thefigure represents the fracture surface of fatigue crack 2.Between the fracture surfaces of fatigue crack 2 andshear failure S2, the surface with coarse fatigue striationsin the middle portion of the figure represents the transi-tion fatigue crack surface due to the abrupt change ofthe crack growth direction as discussed earlier. Fig. 13eshows a smeared surface and some undamaged elongateddimples on the fracture surface S1 where the upper sheetis torn off. As shown in the figure, most of the dimplesare smeared possibly due to the rubbing of the uppersheet.

5. A kinked fatigue crack growth model

In order to develop an engineering fatigue model, weidealize the three-dimensional spot friction weld problem

Life

Loa

d ra

nge

(N)

103

104

105

106

400

800

1200

1600

2000

2400

High-cycle cracking mode, kI(a) and kII(a)Low-cycle cracking mode, kI(a) and kII(a)High-cycle cracking mode, (kI)0 and (kII)0

Low-cycle cracking mode, (kI)0 and (kII)0

Experimental results (flat tool)

Fig. 15. Experimental results and fatigue life estimations for spot frictionwelds made by the flat tool in lap-shear specimens. Symbols represent theexperimental results and various lines represent the fatigue life estimationsbased on Eq. (9) in Part 1 with kI(a) and kII(a) and Eq. (12) in Part 1 with(kI)0 and (kII)0, respectively.

P.-C. Lin et al. / International Journal of Fatigue 30 (2008) 90–105 101

as a two-dimensional crack problem as shown in Fig. 14.Fig. 14a shows a schematic of the cross section of a lap-shear specimen made by the flat tool with the sheet thick-ness t under a statically equivalent combined tensile andbending load. The decomposition of the lap-shear load tofour sets of loads to derive the analytical stress intensityfactor solutions can be found in Lin et al. [19]. Fig. 14bshows a schematic of the dominant fatigue cracking modeof the spot friction weld made by the flat tool under low-cycle loading conditions. Fig. 14c shows a schematic ofthe dominant fatigue cracking mode of the spot frictionweld made by the flat tool under high-cycle loading condi-tions. Note that the fatigue crack growth behaviors of spotfriction welds made by the flat tool under loading condi-tions of low-cycle fatigue (lives of 103–104) and high-cyclefatigue (lives of 104–105) are different as shown in Figs. 8and 11. As shown in Fig. 14b, a kinked fatigue crack,marked as crack 2, is initiated from the original crack tipwith a kink angle a and propagates near the boundary ofthe stir zone. The kink angle a of fatigue crack 2 is esti-mated to be 45� for the spot friction weld under low-cycleloading conditions. As shown in Fig. 14c, a kinked fatiguecrack, marked as crack 1 0, is initiated from the crack tipwith a kink angle a. Another fatigue crack, marked ascrack 2 0, is initiated from the bend surface of the uppersheet. As discussed earlier, the spot friction weld made bythe flat tool under high-cycle loading conditions appearsto be dominated by the kinked fatigue crack 1 0 in the lowersheet. Note that the kink angle a of fatigue crack 1 0 is esti-mated to be 62.5� for the spot friction weld under high-cycle loading conditions.

Based on the experimental observations of the paths ofthe dominant kinked fatigue cracks, the fatigue crackgrowth model presented in Part 1 is adopted to estimate

t

Doubler

Leg 1Stir zo

Leg 1

Stir zo

Crack 1′

Fig. 14. (a) A schematic plot of a lap-shear specimen made by the flat tool withschematic of the dominant fatigue cracking mode of the spot friction weld madthe dominant fatigue cracking mode of the spot friction weld made by the fla

the fatigue lives of the spot friction welds made by the flattool. The detailed discussions of the fatigue life estimationsfor spot friction welds can be found in Part 1.

6. Fatigue life estimations

Fig. 15 shows the experimental results for spot frictionwelds made by the flat tool and the fatigue life estimationsbased on the fatigue crack growth models in Eqs. (9) and(12) in Part 1. The fatigue life estimations for low-cyclefatigue are based on the stress intensity factors for fatiguecrack 2 shown in Fig. 14b. The life estimations are obtained

Doubler

Leg 2

ne

Crack 2

Leg 2ne

Crack 2′

the sheet thickness t under an applied force (shown as bold arrows), (b) ae by the flat tool under low-cycle loading conditions and (c) a schematic oft tool under high-cycle loading conditions.

102 P.-C. Lin et al. / International Journal of Fatigue 30 (2008) 90–105

from the nugget diameter d = 5.88 mm, the upper sheetthickness t = 0.63 mm under the shoulder indentation,and the kink angle a = 45� based on the micrograph shownin Fig. 8. The life estimations are plotted for the larger loadranges applied in the experiments and they are marked asthe low-cycle cracking mode in the figure. Here we arbi-trarily select a load range as the demarcation point forthe low-cycle fatigue cracking mode and the high-cycle fati-gue cracking mode as shown in Fig. 15 without a full scaleinvestigation due to the limited number of the availablespecimens. The fatigue life estimations for high-cycle fati-gue are based on the stress intensity factors for fatiguecrack 1 0 shown in Fig. 14c. The life estimations areobtained from the nugget diameter d = 5.88 mm, the lowersheet thickness t = 0.94 mm, and the kink angle a = 62.5�based on the micrograph shown in Fig. 11a. The life esti-mations are plotted for the smaller load ranges applied inthe experiments and they are marked as the high-cyclecracking mode in the figure. Here, the nugget diameter isdetermined based on the location of the original cracktip. The stress intensity factor solutions discussed in Part1 are adopted. It should be noted that the global and localstress intensity factors depend upon many geometricparameters, such as the nugget diameter, sheet thickness,kink length and kink angle. The stress intensity factor solu-tions discussed in Part 1 are used as approximate solutionsto estimate the fatigue lives. Since the material constants ofthe Paris law for aluminum 6111-T4 are not available, thematerial constants C ¼ 1:35� 10�7 mm=cycle

ðMPaffiffiffi

mpÞm and m = 2.55

for aluminum 6013-T4 [20] are used to estimate the fatiguelives.

As shown in the Fig. 15, the fatigue life estimation forhigh-cycle fatigue based on the global KI and KII solutionsand the local kI(a) and kII(a) solutions in Eq. (9) in Part 1appears to agree well with the experimental results for livesof 104–105. The fatigue life estimation for low-cycle fatigueappears to be a bit higher than the experimental results forlives of 103–104. The fatigue life estimation for high-cyclefatigue based on the global KI and KII solutions and thelocal (kI)0 and (kII)0 solutions in Eq. (12) in Part 1 appearsto be higher than the experimental results for lives of 104–105. The fatigue life estimation for low-cycle fatigueappears to be higher than the experimental results for livesof 103–104. As shown in Fig. 15, the gray bands representthe transition of the fatigue crack growth behaviors fromthe low-cycle cracking mode to the high-cycle crackingmode. For the limited number of specimens available, wecould not determine more precisely the applied load rangefor the transition of one cracking mode to the other.

7. A comparison of the failure modes of two types of welds

Under quasi-static loading conditions, the failure modeshown in Fig. 7a for the spot friction welds made by the flattool is now compared with the failure mode shown inFig. 7a in Part 1 for the spot friction welds made by theconcave tool. Since the tool geometries of the flat and con-

cave tools are different and the processing conditions arealso quite different, the stir zones, the thicknesses of theupper sheet near the weld, and the weld sizes of the spotfriction welds made by these tools are quite different.Apparently, the weld size for the spot friction welds madeby the flat tool is smaller. The small size of the spot frictionwelds and the thin thickness of the upper sheet near theweld give more stress concentration. The low fracture resis-tance of the material near the stir zone allows the crack togrow near the stir zone to cause the final failure of the weld.On the other hand, for the spot friction welds made by theconcave tool, the weld size and the stir zone are quite largeand the weld is almost completely made of the stir zonewith a high fracture resistance. Therefore, the final failureis caused by the necking mechanism of the upper sheet out-side the weld near the location where the thickness appearsto be minimum.

Under low-cycle loading conditions, the failure modeshown in Fig. 8 for the spot friction welds made by the flattool is now compared with the failure mode shown in Fig. 8in Part 1 for the spot friction welds made by the concavetool. For spot friction welds made by the flat tool, the fati-gue crack growth resistance of the material near the stirzone is low under low-cycle loading conditions. The smallweld size and the thin thickness of the upper sheet nearthe weld give more stress concentration. Similar to the fail-ure mode of the weld under quasi-static loading conditions,the low fatigue crack growth resistance of the material nearthe stir zone allows the dominant fatigue crack 2 to grownear the stir zone to cause the final failure of the weldthrough the fracture surface S1. For spot friction weldsmade by the concave tool, the weld is almost completelymade of the stir zone with a high fracture resistance. Thestir zone with a high fatigue crack growth resistance pre-vents the kinked fatigue crack emanating from the crackextended from notch N2 located on the right side of the fig-ure. However, the small radius of the bend surface withhigh stress concentration allows fatigue crack 2 in theupper sheet to emanate from the bend surface B2. In themean time, the dominant kinked fatigue crack 1 in thelower sheet emanates from the original crack extendedfrom notch N1 located on the left side of the figure andgrows through the lower sheet thickness. At the final stageof the failure mode, the final failure of the weld is caused bythe shear failure in the stir zone through the fracture sur-face I2.

Under high-cycle loading conditions, the failure modeshown in Fig. 11 for the spot friction welds made by the flattool is now compared with the failure mode shown inFig. 12 in Part 1 for the spot friction welds made by theconcave tool. For spot friction welds made by the flat tool,the fatigue crack growth resistance of the material near thestir zone is high under high-cycle loading conditions. Thehigh fatigue crack growth resistance of the material pre-vents the fatigue crack emanating from the crack extendedfrom notch N2. However, the small radius of the bend sur-face with high stress concentration allows fatigue crack 2 0

P.-C. Lin et al. / International Journal of Fatigue 30 (2008) 90–105 103

to emanate from the bend surface B2 of the upper sheet.On the other hand, the dominant kinked fatigue crack 1 0

in the lower sheet emanates from the original crack tip nearthe left side of the stir zone and grows through the lowersheet thickness. For spot friction welds made by the con-cave tool, the failure mode is similar to that of spot frictionwelds made by the flat tool. The dominant kinked fatiguecrack 1 in the lower sheet emanates from the original cracktip and another fatigue crack 2 in the upper sheet emanatesfrom the bend surface, marked by B2, as shown in Fig. 12ain Part 1. Both fatigue cracks grow through the thicknessand become transverse through cracks growing in thewidth direction of the specimen to cause the final failureof the specimens. However, for spot friction welds madeby the flat tool as shown in Fig. 12, a nugget pull-out fail-ure is shown, whereas for spot friction welds made by theconcave tool as shown in Fig. 13 in Part 1, the experimentwas stopped and the final failure mode is possibly due tothe transverse cracks growing through the specimen width.

0 0.5 1 1.5 2 2.5 3 3.5 40

0.5

1

1.5

2

2.5

3

Displacement (mm)

Loa

d (k

N)

Concave toolFlat tool

103 104 105 106400

800

1200

1600

2000

2400

Life

Loa

d ra

nge

(N)

Experimental results (Flat tool)Experimental results (Concave tool)

Fig. 16. (a) Typical load–displacement curves of spot friction welds madeby a concave tool and a flat tool under lap-shear loading conditions. (b) Acomparison of the fatigue lives for spot friction welds made by the concavetool and the flat tool in lap-shear specimens. Symbols represent theexperimental results.

Fig. 16a shows the typical load–displacement curves ofthe spot friction welds made by a concave tool and a flattool in lap-shear specimens. Note that the slackness inthe test setup has been removed. The average failure loadsfor the spot friction welds made by the concave tool andthe flat tool is 2.59 and 1.94 kN, respectively. Fig. 16bshows a comparison of the experimental fatigue lives forspot friction welds made by the concave tool and the flattool in lap-shear specimens. As shown in Fig. 16a, the max-imum failure load is larger for the spot friction welds madeby the concave tool. As expected, the spot friction weldsmade by the concave tool have longer fatigue lives underlarge load ranges. The performance of the welds made bythe concave tool in terms of fatigue life is better as indi-cated in Fig. 16a. However, the trends of the experimentalresults for the two types of spot friction welds in Fig. 16aare quite different. At large load ranges, the fatigue livesof the spot friction welds made by the flat tool appear tobe shorter than those made by the concave tool. However,at small load ranges, the fatigue lives of the spot frictionwelds made by the flat tool appear to become close to thosemade by the concave tool due to the different trends. Itseems that the spot friction welds made by the flat toolmay perform better at even smaller load ranges if the trendsof the experimental results can be extrapolated to longerfatigue lives. Further experimental works are needed to val-idate the trends. Therefore, the failure strengths of spotfriction welds under quasi-static loading condition can beused cautiously as references. However, fatigue tests mustbe performed to validate the performance of spot frictionwelds under cyclic loading conditions.

8. Discussions

Based on experimental observations, the macroscopicshapes of the failed spot friction welds made by the flat toolunder quasi-static and cyclic loading conditions are similar.However, the microscopic features on the fracture surfacesof these failed spot friction welds are quite different. Underquasi-static loading conditions, dimples can be seen on thefracture surface of crack 2, as shown in Fig. 7b. These dim-ples came from void nucleation, growth and coalescence.Under cyclic loading conditions, both dimples and fatiguestriations can be seen on the fracture surface of fatiguecrack 2, as show in Figs. 10c and 13c. Based on the workof Broek [21] and El-Soudani and Pelloux [22], this typeof fracture surface often occurs when the plastic deforma-tion near the crack tip is large under a large driving forcesuch as a large stress intensity factor. In general, voidsare nucleated from the particles or inclusions in front ofthe crack tip when the driving force such as the stress inten-sity factor is large. The material between the voids and thecrack tip can reach the instability and rupture by voidnucleation, growth and coalescence. Under the circum-stances, fatigue striations become very rare and the fracturesurface consists primarily of dimples, as shown in Figs. 10cand 13c.

104 P.-C. Lin et al. / International Journal of Fatigue 30 (2008) 90–105

Based on the work of Broek [23], the elongated dimpleson the fracture surface indicate the final fracture process asshown in the upper portion of Figs. 10d and 13d. Thecoarse fatigue striations as shown in the middle portionsof these figures may represent the crack growth behaviorduring the abrupt change of the crack growth direction justbefore the final fracture. The abrupt change of the fatiguecrack growth direction indicates that the material fatigueresistance in the new direction may be more favorable forcontinued crack growth. The fatigue striations appear pos-sibly due to the change of the local driving force and/or thelocal microstructure. We have made estimations of thelocal stress intensity factors for fatigue crack 2 and the sec-ond kinked crack from fatigue crack 2 to the final shearfailure S2 based on Eqs. (3) and (4) and the computationalresults in Fig. 17 in Part 1. Fatigue crack 2 grows undernearly pure mode I conditions. When the second kinkedcrack occurs before the final shear failure S2, the localstress intensity factor at the second kinked crack tip haveonly about 50% of the mode I stress intensity factor beforethe kinked crack occurs. The driving force is significantlyreduced and, consequently, the fatigue striations becomethe dominant feature on the fracture surface. The widerspacing of these coarse fatigue striations indicates thatthe material near the crack tip is under large plastic defor-mation for each cycle of loading. Note that the small dim-ples, as shown in the lower portion of Figs. 10d and 13dcame from the growth of fatigue crack 2 as discussed ear-lier. It should be mentioned that we also observe an abruptchange of the crack growth direction under quasi-staticloading conditions as shown in Fig. 7. However, no frac-ture surface with the features similar to the coarse fatiguestriations as shown in Figs. 10d and 13d can be foundunder quasi-static loading conditions.

As shown in Fig. 15, the estimated fatigue lives of spotfriction welds made by the flat tool based on the globalKI and KII solutions and the local (kI)0 and (kII)0 solutionsin Eq. (12) in Part 1 are higher than those based on the glo-bal KI and KII solutions and the local kI(a) and kII(a) solu-tions in Eq. (9) in Part 1 because the local (keq)0 is smallerthan keq(a). The detailed discussions for the effects of thekink length a on the local stress intensity factors and fati-gue life estimations of the fatigue crack growth modelscan be found in Part 1.

As shown in Fig. 15, the magnitudes of the slopes of thefatigue life estimations, which are determined by the valueof m, are higher than that of the experimental results. Asshown in the figure, the fatigue life estimations for high-cycle fatigue based on the global K solutions and the localkI(a) and kII(a) solutions in Eq. (9) in Part 1 agrees wellwith the fatigue lives of spot friction welds under high-cycleloading conditions. However, the fatigue life estimationsfor low-cycle fatigue based on the global K solutions andthe local kI(a) and kII(a) solutions in Eq. (9) in Part 1 area bit higher than the fatigue lives of spot friction weldsunder low-cycle loading conditions. For spot friction weldsunder low-cycle loading conditions, fatigue crack 2 propa-

gates near the boundary of the stir zone as shown in Fig. 8.Therefore, one possible reason is that the material near theboundary of the stir zone has a relatively low fatigue crackgrowth resistance when the load amplitude is high underlow-cycle loading conditions. Another possible reason isthat the material constants C and m of aluminum 6111-T4 are different from those of aluminum 6013-T4.

9. Conclusions

Failure modes of spot friction welds made by a flat toolin lap-shear specimens of aluminum 6111-T4 sheets areinvestigated based on the approach presented in Part 1.Optical and scanning electron micrographs of the weldsbefore and after failure under quasi-static and cyclic load-ing conditions are examined. The micrographs show thatthe microstructure, geometry and the failure modes of thewelds made by the flat tool are quite different from thoseof the welds made by a concave tool. Under quasi-staticloading conditions, the failure mainly starts from crackingnear the boundary of the stir zone close to the upper sheetsurface inside the weld. Under cyclic loading conditions,the experimental results indicate three types of fatiguecracks. The first type initiates and grows near the boundaryof the stir zone close to the upper sheet surface inside theweld as that under quasi-static loading conditions. The sec-ond type initiates and grows into the lower sheet outsidethe stir zone. The third type initiates from the bend surfaceof the upper sheet outside the weld. Under low-cycle load-ing conditions, the dominant kinked fatigue cracks are thefirst type growing near the boundary of the stir zone.Under high-cycle loading conditions, the dominant kinkedfatigue cracks are the second type growing in the lowersheet outside the stir zone. Based on the experimentalobservations of the paths of the dominant kinked fatiguecracks, the fatigue crack growth model presented in Part 1is then adopted to estimate the fatigue lives of the spotfriction welds made by the flat tool. The fatigue life estima-tions based on the fatigue crack growth model with the glo-bal and local stress intensity factors as functions of thekink length and the experimentally determined kink anglesagree well with the experimental results. A comparison ofthe experimental results suggests that the failure strengthsof spot friction welds under quasi-static loading conditioncan cautiously be used as references to select a tool andthe corresponding processing parameters. However, fatiguetests must be performed to validate the performance ofspot friction welds under cyclic loading conditions.

Acknowledgements

The support of this work by the Ford University Re-search Program and the National Science Foundation un-der Grant No. DMI-0456755 is greatly appreciated. Thesupport of the research work on spot friction welds fromDr. C. Wu and Dr. C. Johnson of Ford Motor Companyis greatly appreciated. The help from Mr. J.M. Nicholson

P.-C. Lin et al. / International Journal of Fatigue 30 (2008) 90–105 105

of Ford Motor Company and Mr. M.A. Garman and Mr.E. Carrier of Kawasaki Robotics (USA), Inc. on the spotfriction welding process and the metallurgy work is alsogreatly appreciated. Helpful discussions with Dr. S.-H.Lin of China Motor Corporation, Dr. D.S. Taylor ofArvinMeritor Inc. and Dr. P. Friedman of Ford MotorCompany are greatly appreciated. The assistance of Mr.S.-S. Li of University of Michigan on taking scanning elec-tron micrographs is also greatly appreciated.

References

[1] Sakano R, Murakami K, Yamashita K, Hyoe T, Fujimoto M,Inuzuka M, et al. Development of spot FSW robot system forautomobile body members. In: Proceedings of the third internationalsymposium of friction stir welding; 2001.

[2] Iwashita T. Method and apparatus for joining. US Patent 660,1751B2, August, 5, 2003.

[3] Lin P-C, Lin S-H, Pan J, Pan T, Nicholson JM, Garman MA.Microstructures and failure mechanisms of spot friction welds in lap-shear specimens of aluminum 6111-T4 sheets. SAE Technical PaperNo. 2004-01-1330. Warrendale, PA: Society of Automotive Engi-neers; 2004.

[4] Pan T, Joaquin A, Wilkosz DE, Reatherford L, Nicholson JM, FengZ, et al. Spot friction welding for sheet aluminum joining. In:Proceedings of the fifth international symposium of friction stirwelding; 2004.

[5] Fujimoto M, Inuzuka M, Nishio M, Nakashima Y. Development offriction spot joining (Report 1) – cross sectional structures of frictionspot joints. The National Meeting of Japan Welding Society, No. 74;2004. p. 4–5.

[6] Fujimoto M, Inuzuka M, Nishio M, Nakashima Y. Development offriction spot joining (Report 2) – mechanical properties of frictionspot joints. The National Meeting of Japan Welding Society, No. 74;2004. p. 6–7.

[7] Hinrichs JF, Smith CB, Orsini BF, DeGeorge RJ, Smale BJ, RuehlPC. Friction stir welding for the 21st century automotive industry. In:Proceedings of the fifth international symposium of friction stirwelding; 2004.

[8] Mitlin D, Radmilovic V, Pan T-Y, Chan J, Feng Z, Santella ML.Structure–properties relations in spot friction welded (also known asfriction stir spot welded) 6111 aluminum. Mater Sci Eng A2006;441:79–96.

[9] Pook LP. Fracture mechanics analysis of the fatigue behaviour ofspot welds. Int J Fract 1975;11:173–6.

[10] Swellam MH, Banas G, Lawrence FV. A fatigue design parameter forspot welds. Fatigue Fract Eng Mater Struct 1994;17:1197–204.

[11] Zhang S. Stress intensities at spot welds. Int J Fract 1997;88:167–85.[12] Zhang S. Fracture mechanics solutions to spot welds. Int J Fract

2001;112:247–74.[13] Newman JA, Dowling NE. A crack growth approach to life

prediction of spot-welded lap joints. Fatigue Fract Eng Mater Struct1998;21:1123–32.

[14] Pan N, Sheppard SD. Stress intensity factors in spot welds. Eng FractMech 2003;70:671–84.

[15] Wang D-A, Lin P-C, Pan J. Geometric functions of stress intensityfactor solutions for spot welds in lap-shear specimens. Int J SolidsStruct 2005;42:6299–318.

[16] Wang D-A, Lin S-H, Pan J. Stress intensity factors for spot welds andassociated kinked cracks in cup specimens. Int J Fatigue2005;27:581–98.

[17] Wang D-A, Pan J. a computational study of local stress intensityfactor solutions for kinked cracks near spot welds in lap-shearspecimens. Int J Solids Struct 2005;42:6277–98.

[18] Lin S-H, Pan J, Wung P, Chiang J. A fatigue crack growth model forspot welds in various types of specimens under cyclic loadingconditions. Int J Fatigue 2006;28:792–803.

[19] Lin P-C, Wang D-A, Pan J. Mode I stress intensity factor solutionsfor spot welds in lap-shear specimens. Int J Solids Struct2007;44:1013–37.

[20] Bergner F, Zouhar G. A new approach to the correlation between thecoefficient and the exponent in the power law equation of fatiguecrack growth. Int J Fatigue 2000;22:229–39.

[21] Broek D. The effect of intermetallic particles on fatigue crackpropagation in aluminum alloys. In: Pratt PL (editor-in-chief),Fracture 1969, proceedings of the second international conferenceon fracture; 1969. p. 754–64.

[22] El-Soudani SM, Pellouz RM. Influence of inclusion content onfatigue crack propagation in aluminum alloys 1973;4:519–31.

[23] Broek D. The role of inclusions in ductile fracture and fracturetoughness. Eng Fract Mech 1973;5:55–66.