Failure modes and fatigue life estimations of spot friction welds in lap-shear specimens of aluminum...

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International Journal of Fatigue 30 (2008) 74–89

JournalofFatigue

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

Part 1: Welds made by a concave 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 concave tool in lap-shear specimens of aluminum 6111-T4 sheets are first investigatedbased on experimental observations. Optical and scanning electron micrographs of the welds before and after failure under quasi-staticand cyclic loading conditions are examined. The micrographs show that the failure modes of the welds under quasi-static and cyclic load-ing conditions are quite different. Under quasi-static loading conditions, the failure mainly starts from the necking of the upper sheetoutside the weld. Under cyclic loading conditions, the experimental observations indicate two types of fatigue cracks. One type initiatesand grows into the lower sheet outside the stir zone and another type initiates from the bend surface of the upper sheet outside the weld.The dominant fatigue cracks for the final failures of the welds are the kinked fatigue cracks growing in the lower sheet outside the stirzone. Based on the experimental observations of the paths of the dominant kinked fatigue cracks, a fatigue crack growth model is thenadopted to estimate the fatigue lives of the spot friction welds. The global stress intensity factors and the local stress intensity factors forkinked cracks based on the recent published works for resistance spot welds and the Paris law for crack propagation are used in thefatigue crack growth model. The fatigue life estimations based on the fatigue crack growth model with the global and local stress inten-sity factors as functions of the kink length and the experimentally determined kink angles agree well with the experimental results.� 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

A rapid development of applications of lightweightmaterials in the automotive industry is reflected in theincreasing use of aluminum and magnesium alloys. Manycomponents produced from these alloys, by stamping, cast-ing, extrusion and forging, have to be joined as part ofmanufacturing processes. Resistance spot welding is themost commonly used joining technique for body-in-whiteparts made of steel sheets. However, resistance spot weld-

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

doi:10.1016/j.ijfatigue.2007.02.016

* Corresponding author. Tel.: +1 734 764 9404; fax: +1 734 647 3170.E-mail address: [email protected] (J. Pan).

ing of aluminum sheets is likely to produce poor welds asreported by Thornton et al. [1] and Gean et al. [2].Recently, a new spot friction welding (SFW) technologyfor joining aluminum sheets has been developed by MazdaMotor Corporation and Kawasaki Heavy Industry [3,4].

A schematic illustration of the new spot friction weldingprocess is shown in Fig. 1(a). The process is applied to jointhe two metal sheets as shown. A rotating tool with a probepin is first plunged into the upper sheet. When the rotatingtool contacts the upper sheet, a downward force is applied.A backing tool beneath the lower sheet is used to supportthe tool downward force. The tool downward force andthe tool rotational speed are maintained for an appropriate

mailto:[email protected]

Plunging Bonding Drawing out

Tool

Probe pin

Concaveshoulder

Tool

Probe pin

Flatshoulder

a

b

Fig. 1. (a) A schematic illustration of spot friction welding process, (b) amagnified cross sectional view of the tool tip with a concave shoulder and(c) a magnified cross sectional view of the tool tip with a flat shoulder.

F F

Doubler

Doubler

AB CD

dV

W

t

L

Fig. 2. A schematic of a lap-shear specimen with a resistance spot weld.The weld nugget is idealized as a circular cylinder as shown in the figure.

P.-C. Lin et al. / International Journal of Fatigue 30 (2008) 74–89 75

time to generate frictional heat. Then, heated and softenedmaterial adjacent to the tool deforms plastically, and asolid state bond is made between the surfaces of the upperand lower sheets. Finally, the tool is drawn out of thesheets as shown. Figs. 1(b) and (c) show magnified crosssectional views of the tool tips with a concave shoulderand a flat shoulder, respectively. Research results for weldsmade by a concave tool are reported in Part 1 and those forwelds made by a flat tool are reported in Part 2. For thespot friction welding process, the important processingvariables are the tool geometry, the tool rotational speed,the tool holding time and the tool downward force. Theresearch results reported here are for the welds which weremade based on a DOE (design of experiments) method todetermine the optimum tool rotational speed, tool holdingtime and tool downward force for the maximum failurestrengths of the welds in lap-shear specimens.

The microstructures and failure modes of spot frictionwelds under quasi-static loading conditions have been stud-ied based on experimental observations. For example, Linet al. [5] studied the microstructures and failure modes ofspot friction welds in lap-shear specimens of aluminum6111-T4 sheets using optical micrographs. Pan et al. [6]and Fujimoto et al. [7,8] examined the failure modes ofspot friction welds in lap-shear specimens based on micro-graphs and micro hardness distributions. The results ofPan et al. [6] and Fujimoto et al. [7,8] indicate that failureloads and failure modes depend on the tool indentationdepth. Hinrichs et al. [9] used a DOE (design of experi-ments) method to determine optimum processing parame-ters for the failure strengths of spot friction welds in lap-shear and cross-tension specimens of aluminum 5754-Osheets with considerations of different tools. The micro-graphs in Lin et al. [5], Pan et al. [6] and Fujimoto et al.[7] show that the spot friction welds have no apparent largemacroscopic defect in the stir zone when compared with

the large voids shown in the aluminum resistance spotwelds as reported in Thornton et al. [1] and Gean et al.[2]. Recently, the metallurgical aspects of aluminum 6111-T4 spot friction welds were investigated by Mitlin et al.[10].

Since the fatigue behaviors of spot friction welds havenot been widely investigated from the fracture mechanicsviewpoint, we here review some past relevant researchworks on the fatigue behaviors of resistance spot weldsbased on fracture mechanics. Fig. 2 schematically showsa lap-shear specimen with a resistance spot weld. Theapplied force F is shown as the bold arrows. The weld nug-get is idealized as a circular cylinder. The lap-shear speci-men has the sheet thickness t, the specimen width W, thenugget diameter d, the sheet length L, and the overlaplength V of the upper and lower sheets. The critical loca-tions with the maximum values of mode I and II stressintensity factors are marked as point A and point B. Thecritical locations with the maximum value of mode IIIstress intensity factors are marked as point C and pointD. From the viewpoint of fracture mechanics, Pook [11]gave the stress intensity factors at the critical locations ofresistance spot welds in lap-shear specimens. Swellamet al. [12] proposed a stress index Ki based on their stressintensity factor solutions to model their experimentalresults. Zhang [13,14] obtained the stress intensity factorsof resistance spot welds in order to correlate the fatiguebehaviors of resistance spot welds in different types of spec-imens. Wang et al. [15] proposed the geometric functionsfor the global stress intensity factors of resistance spotwelds in lap-shear specimens based on the results of theirthree-dimensional finite element computations and theclosed-form solutions for a finite plate with a rigid inclu-sion. Note that the global stress intensity factors dependon many geometric parameters of lap-shear specimens,such as the nugget diameter, sheet thickness, specimenwidth, sheet length, and overlap length [15].

Newman and Dowling [16] adopted Pook’s global stressintensity factors to develop a fatigue model to estimate thefatigue lives of resistance spot welds in lap-shear specimensbased on a crack growth approach with consideration ofthe local stress intensity factors for kinked cracks. Linet al. [17] adopted various global stress intensity factorsto develop a fatigue model to estimate the fatigue lives ofresistance spot welds in various specimens based on a crackgrowth approach with considerations of the local stressintensity factors for kinked cracks. The results indicatedthat the fatigue model based on the global stress intensity

76 P.-C. Lin et al. / International Journal of Fatigue 30 (2008) 74–89

factors of Zhang [13,14], Pook [11], and Wang et al. [18]appears to be able to characterize the fatigue lives of resis-tance spot welds in square cup, coach-peel and lap-shearspecimens.

For kinked cracks, when the kink length approaches to0, the local stress intensity factors can be expressed as func-tions of the kink angle and the global stress intensity fac-tors for the main crack [19,20]. Newman and Dowling[16] and Lin et al. [17] assumed that the local stress inten-sity factors of resistance spot welds are independent ofthe kink length for fatigue life estimations based on a crackgrowth approach. However, Pan and Sheppard [21], Wanget al. [18], and Wang and Pan [22] indicated that the localstress intensity factors of resistance spot welds depend onthe kink length based on their three-dimensional finite ele-ment computations for lap-shear and cup specimens.

In this paper, failure modes of spot friction welds in alu-minum 6111-T4 lap-shear specimens are first investigatedbased on experimental observations. A concave tool wasused to make the spot friction welds investigated here.Optical and scanning electron micrographs of the spot fric-tion welds before and after failure under quasi-static andcyclic loading conditions are examined. The failure modesof the spot friction welds under quasi-static, low-cycle andhigh-cycle loading conditions are then investigated. Thedominant fatigue cracks for the spot friction welds areidentified. Based on the experimental observations of thepaths of the dominant kinked fatigue cracks, a fatiguecrack growth model of Newman and Dowling [16] andLin et al. [17] is then adopted to estimate the fatigue livesof the spot friction welds. The global stress intensity factorsolutions of Wang et al. [15] and the local stress intensityfactor solutions of Wang and Pan [22] for kinked cracksand the Paris law for fatigue crack propagation are usedin the fatigue crack growth model. Finally, the life estima-tions based on the fatigue crack growth model with theexperimentally determined kink angles are compared withthe experimental results for the spot friction welds in lap-shear specimens.

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 tool with a concaveshoulder as schematically shown in Fig. 1(b) was used tomake the spot friction welds investigated here. Fig. 3 showsa cross sectional view and close-up views of a spot frictionweld made by the concave tool before testing. Fig. 3(a)shows an optical micrograph of the cross section. As shownin the figure, the indentation profile reflects the shape of theprobe pin and the concave tool shoulder of the tool. Theplunge depth can be estimated from the indentation profileas 1.54 mm for this particular weld. The bottom surface iskept almost flat except near the center hole. Near the cen-tral hole, two large gray areas represent the fine grain stirzones where the upper and lower sheets are bonded. Thegray stir zone extends out along the interfacial plane about

3 mm from the central hole profile. Two notches, markedas N1 and N2, can be seen in the figure. Fig. 3(b) showsa close-up optical micrograph of region I where the notch,marked as N1, extends and becomes a crack. The locationof the crack tip is marked in the figure. As shown in the fig-ure, the interfacial surfaces become zigzag and graduallydisappear into the stir zone. Note that the nugget diametercan be determined based on the location of the originalcrack tip. The nugget diameter is estimated to be7.69 mm. Fig. 3(c) shows a close-up scanning electronmicrograph of region II where the zigzag interface inFig. 3(b) is now seen as strips of voids. The strips of voidscan be seen clearly from a close-up scanning electronmicrograph in Fig. 3(d). Fig. 3(e) shows a scanning electronmicrograph of a void with oxides on the void surface. Notethat during the spot friction welding process, the materialnear the interfacial surfaces is under high pressure andlarge plastic deformation. The interface region is distortedinto a region with strips of voids as shown in Fig. 3(d).Note that the voids have oxides on the void surfaces.Between the voids, the material near the zigzag interfacialsurface appears to be well bonded together. A detailed dis-cussion of the metallurgical aspects of aluminum 6111-T4spot friction welds made by a flat tool can be found in Mit-lin et al. [10].

As shown in Fig. 3(a), the thickness of the weld nuggetnear the central hole is much larger than that near the outercircumference of the shoulder indentation due to the con-cave tool shoulder. The concave tool shoulder squeezedout some upper sheet material but maintained some uppersheet material near the central hole. The shoulder indenta-tion resulted in a radial expansion of the upper sheet alongthe outer circumference of the shoulder indentation. How-ever, due to the constraint of the neighboring material, thesheet was therefore bent along the outer circumference ofthe shoulder indentation. In Fig. 3(a), the bend is markedas B1 and B2.

3. Experiments

Lap-shear specimens were made by using two 25.4 mmby 101.6 mm sheets with a 25.4 mm by 25.4 mm overlaparea. Fig. 4(a) shows a lap-shear specimen with a spot fric-tion weld made by the concave tool. As shown in the figure,two doublers are made by folding two square parts of thesheets near the ends (25.4 mm · 25.4 mm). Note that thedoublers are used to align the applied load to avoid the ini-tial realignment of the specimen under lap-shear loadingconditions. Lap-shear specimens were first tested by usingan Instron 4502 testing machine at a monotonic displace-ment rate of 1.0 mm per minute. The tests were terminatedwhen specimens separated. The load and displacementwere simultaneously recorded during the testing. Fig. 4(b)shows a typical load–displacement curve of a spot frictionweld made by the concave tool under lap-shear loadingconditions. Note that the slackness in the test setup has

Fig. 3. (a) An optical micrograph of the cross section of a spot friction weld made by the concave tool, (b) a close-up optical micrograph of region I, (c) aclose-up scanning electron micrograph of region II, (d) a close-up scanning electron micrograph of the strips of voids as shown in (c), (e) a close-upscanning electron micrograph of the void as shown in (c).


been removed. The average failure load for tested speci-mens is 2.59 kN. The lap-shear specimens were then testedby using an Instron servo-hydraulic fatigue testing machinewith the load ratio R of 0.2. The test frequency was 10 Hz.The tests were terminated when specimens separated, ornearly separated when the displacement of the two gripsof specimens exceeded 5 mm. Fig. 5 shows the experimentalresults for the spot friction welds made by the concave toolin lap-shear specimens under cyclic loading conditions.

4. Failure modes under quasi-static and cyclic loadingconditions

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 different failure mode. The

failed 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, low-cycle fatigue (lives of 103–104) and high-cycle fati-gue (lives of 104–105).

Fig. 6(a) shows a schematic plot of the cross sectionalong the symmetry plane of a lap-shear specimen madeby the concave tool with the sheet thickness t under anapplied load (shown as the bold arrows). Fig. 6(b) showsa schematic plot of the cross section near the spot frictionweld under a statically equivalent combined tension andbending load. In these figures, the shadow represents thestir zone, the short dash lines near the two notches repre-sent the unwelded interfacial surface, and the thin solidlines represent either fracture surface or fatigue crack.Fig. 6(c) shows a table which summarizes the failure modesof the spot friction welds under quasi-static, low-cycle andhigh-cycle loading conditions.

0 0.5 1.5 2.5 3 3.5 40

0.5

1

1.5

2

2.5

3

Displacement (mm)

Loa

d (k

N)

1 2

Fig. 4. (a) A lap-shear specimen with a spot friction weld made by the concave tool, (b) a typical load–displacement curve of a spot friction weld made bythe concave tool under lap-shear loading conditions.


As shown in Fig. 6(b) and as summarized in Fig. 6(c),under quasi-static loading conditions, a necking failure isinitiated at location A, the failure then propagates alongthe nugget circumference, and finally the upper sheet istorn off at location B. Under low-cycle loading conditions,the experimental observations suggest that one fatiguecrack (marked by C) appears to emanate from the originalcrack tip and then another fatigue crack (marked by D)appears to emanate from the bend surface. The experimen-tal observations suggest that the fatigue crack (marked byC) appears to be the dominant crack that propagatesthrough the sheet thickness. Without the support of thelower sheet near the stretching side of the nugget, the nug-get is rotated clockwise and the sheets near the nugget aretherefore bent. Eventually, the stir zone is separatedthrough the interfacial surface (marked by E) and theupper sheet is torn off. Under high-cycle loading condi-

tions, the experimental observations suggest that one fati-gue crack (marked by C) appears to emanate from theoriginal crack tip and another fatigue crack (marked byD) appears to emanate from the bend surface. Both fatiguecracks propagate through the sheet thickness, then becometransverse through cracks growing toward the width direc-tion of the specimens, and finally cause the fracture of thespecimen. In the following, we present micrographs toshow the details of the failure modes of spot friction weldsin lap-shear specimens under different loading conditions.

4.2. Failure mode under quasi-static loading conditions

Fig. 7(a) shows an optical micrograph of the cross sec-tion along the symmetry plane of a partially failed spotfriction weld made by the concave tool under quasi-staticincreasing loading conditions. The arrows in Fig. 7(a) sche-

103 104 105 106400

800

1200

1600

2000

2400

Life

Loa

d ra

nge

(N)

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

t

Doubler

Doubler

Leg 2

Leg 1

Stir zone

ABC

D

EE

Failure mode Quasi-static A B

Low-cycle fatigue C, D EHigh-cycle fatigue C, D Transverse through cracks

→→

→

Fig. 6. (a) A schematic plot of a lap-shear specimen made by the concavetool with the sheet thickness t under an applied force (shown as boldarrows), (b) a schematic plot of the cross section near the spot frictionweld made by the concave tool and (c) the failure modes of spot frictionwelds made by the concave tool under quasi-static, low-cycle and high-cycle loading conditions.


matically show the direction of the applied load. Note thatdue to the extensive plastic deformation in the final failurestage, the nugget rotated clockwise. The loads are thereforemarked schematically parallel to the legs as shown. Theapplied load stretches the upper right sheet (marked asLeg 2) and the lower left sheet (marked as Leg 1). As shownin Fig. 7(a), near the upper right portion of the spot frictionweld, a necking failure, marked by F2, appears between theouter circumference of the shoulder indentation and theoriginal crack tip. Fig. 7(b) shows a close-up scanning elec-tron micrograph of region I on the fracture surface asmarked in Fig. 7(a) from another failed specimen. The dim-ples on the fracture surface indicate the ductile fractureprocess of the necking failure. This necking failure by shear

localization of the spot friction weld is quite similar to thenecking failure of the resistance spot welds in dual phasesteel sheets as discussed in Lin et al. [23]. Macroscopic pic-tures of failed spot friction welds can be found in Lin et al.[5].

4.3. Failure mode under low-cycle loading conditions

Fig. 8 shows an optical micrograph of the cross sectionalong the symmetry plane of a partially failed spot frictionweld made by the concave tool at the fatigue life of nearly103. The arrows in Fig. 8 schematically show the directionof the applied load. Two fatigue cracks can be seen inFig. 8. Near the lower left portion of the spot friction weld,a fatigue crack (marked as crack 1) appears to emanatefrom the original crack tip and propagate through the sheetthickness. Near the upper right portion of the spot frictionweld, another fatigue crack (marked as crack 2) appears toemanate from the bend surface, marked as B2. Note thatfatigue crack 1 has grown through the sheet thickness. Asshown in Fig. 8, an interfacial failure, marked as I2, canbe seen in the right portion of the stir zone. Based on theexperimental observations of failed spot friction welds,fatigue crack 1 can be considered as the main crack tocause the final failure of the spot friction weld. The micro-graphs of the interfacial failure will be seen by the micro-graphs presented later.

Here we present several macroscopic pictures of a failedspot friction weld. Fig. 9(a) shows the lower sheet of afailed lap-shear specimen with a spot friction weld madeby the concave tool at the fatigue life of nearly 103. Theinterfacial failure mode can be seen from the spot frictionweld on the lower sheet of the failed specimen inFig. 9(a). Figs. 9(b) and (c) show the top view and the bot-tom view of the spot friction weld on the lower sheet of thefailed specimen, respectively. As shown in Figs. 9(a)–(c), alarge fatigue crack can be seen along the left portion of thenugget circumference. Note that the large fatigue crack onthe lower sheet of the failed specimen corresponds to fati-gue crack 1 as shown in Fig. 8. The rough surface nearthe outer circumference of the spot friction weld betweena large circle and a small ellipse marked in Fig. 9(b) repre-sents the unwelded surface. The roughness of the surface ispossibly due to the contact and rubbing from the uppersheet during the welding process. The rough surface inthe smaller marked ellipse in Fig. 9(b) represents the lowerfracture surface of the zigzag interfacial crack as indicatedin Fig. 8. Figs. 9(d) and (e) show the top view and the bot-tom view of the spot friction weld on the upper sheet of thefailed specimen, respectively. In Figs. 9(d) and (e), the holerepresents the central hole of the weld due to the penetra-tion of the probe pin through the upper sheet. As shownin Figs. 9(d) and (e), a small fatigue crack can be seen alongthe bend surface. This fatigue crack grows along the outercircumference of the weld, propagates through the uppersheet thickness and becomes the fatigue crack shown inFig. 9(d) on the top surface of the upper sheet. Note that

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

Fig. 8. An optical micrograph of the cross section along the symmetry plane of a partially failed spot friction weld made by the concave tool at the fatiguelife of nearly 103.


this small fatigue crack corresponds to fatigue crack 2 asshown in Fig. 8. As shown in Fig. 9(e), a surface is pro-truded out of the bottom surface of the upper sheet dueto the shoulder indentation. The rough surface in a markedcircle outside the central probe pin hole corresponds to theupper fracture surface of the zigzag interfacial crack asshown in Fig. 8.

Fig. 10(a) shows a micrograph of the cross section alongthe symmetry plane of a failed spot friction weld made bythe concave tool in the lower sheet of a failed specimen at

the fatigue life of nearly 103. The upper part of the weldwas removed for easy access of the surfaces for scanningelectron micrographs. The large bold arrow in Fig. 10(a)schematically shows the direction of the applied load tothe lower sheet. Fig. 10(b) shows a scanning electronmicrograph on the fracture surface of fatigue crack 1 fromanother failed specimen and Fig. 10(c) shows a close-upscanning electron micrograph of region I in Fig. 10(b).The bold arrows in these figures schematically show thepropagation directions of the macroscopic fatigue crack

Fig. 9. (a) A failed spot friction weld lap-shear specimen made by the concave tool at the fatigue life of nearly 103, (b) a top view of a spot friction weld onthe 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 top view of a spot frictionweld 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.


fronts. Fig. 10(b) shows a rough fracture surface of thekinked fatigue crack 1. The black material in the lower por-tion of the figure is the conductive tape used to attach thespecimen to the viewing area of the scanning electronmicroscope. As shown in Fig. 10(c), both fatigue striationsand tear ridges can be seen on the fracture surface of fati-gue crack 1.

Fig. 10(d) shows a scanning electron micrograph on thefracture surface of the interfacial fracture surface I2 fromanother failed specimen and Fig. 10(e) shows a close-upscanning electron micrograph of region II in Fig. 10(d).Fig. 10(d) shows a rough fracture surface of the interfacialfailure I2. As shown in Fig. 10(e), fatigue striations, markedby a, and dimples can be seen on the interfacial fracture sur-face I2. Fatigue striations, marked by a, can be seen in theupper portion of the fracture surface. Several large inclu-sions, marked by b, can be seen in large dimples. A wavy

structure oriented nearly in the horizontal direction can alsobe seen in the figure. Note that the features of the wavystructure and fatigue striations are quite similar to theseobserved on the fracture surfaces of the welds made by a flattool as discussed in Part 2. The wavy structure may comefrom the microstructure of the weld due to the processingconditions. The mixed dimples and fatigue striations maycome from the high stress intensity factor amplitude whichinduces more plastic deformation ahead of the crack tip toresult in more dimples than fatigue striations [24].

4.4. Failure mode under high-cycle loading conditions

Since the failure mode of the spot friction welds at fati-gue life of nearly 105 is quite complex, we need define thelocation of the material point near a spot friction weld withrespect to the loading direction in order to clearly explain

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 theconcave tool at the fatigue life of nearly 103, (b) a scanning electron micrograph of the fracture surface of fatigue crack 1, (c) a close-up scanning electronmicrograph of region I, (d) a scanning electron micrograph of the interfacial fracture surface I2 and (e) a close-up scanning electron micrograph of regionII.

OAE

B

C

D

45o

0o

90o

135o

180o

Loadingdirection

Fig. 11. A top view of a spot friction weld on the upper sheet. The boldarrow shows the loading direction of the upper sheet. The directions ofOA, OB, OC, OD and OE are 0�, 45�, 90�, 135� and 180� with respect tothe loading direction of the upper sheet, respectively.


the failure modes. Fig. 11 schematically shows a top viewof a spot friction weld on the upper sheet. The bold arrowin Fig. 11 schematically shows the loading direction of theupper sheet. The directions of OA, OB, OC, OD and OEare 0�, 45�, 90�, 135� and 180� with respect to the loadingdirection of the upper sheet, respectively. Note that thedirection of OE is the loading direction of the lower sheet.

Fig. 12(a) shows a micrograph of the cross section alongthe symmetry plane of a partially failed spot friction weldmade by the concave tool at the fatigue life of nearly 105.The arrows in Fig. 12(a) schematically show the directionof the applied load. Two fatigue cracks can be seen inFig. 12(a). Near the lower left portion of the spot frictionweld, a fatigue crack, marked as crack 1, appears to ema-nate from the original crack tip of the spot friction weld.Near the upper right portion of the spot friction weld,another fatigue crack, marked as crack 2, appears to ema-nate from the bend surface, marked as B2. These two fati-

Fig. 12. (a) An optical micrograph of the cross section along the symmetry plane of a partially failed spot friction weld made by the concave tool at thefatigue life of nearly 105, (b) optical micrographs of a partially failed spot friction weld cross sectioned in the directions of OB, OC, and OD, respectively.The directions of OB, OC, and OD are 45�, 90� and 135� with respect to the loading direction of the upper sheet, respectively.


gue cracks appear to emanate from the identical locationsas those shown in Fig. 8. The experimental observationsindicate that fatigue crack 1 can damage a larger angularspan of the nugget circumference than fatigue crack 2.Therefore, fatigue crack 1 can be considered as a kinkedcrack emanating from the original crack tip. A similar fail-ure mode was observed in the resistance spot weld lap-shear specimens in mild steel, high strength steel and dualphase steel [17,25,26].

Fig. 12(b) shows micrographs of a partially failed spotfriction weld cross sectioned in the directions of OB, OC,and OD, respectively. The directions of OB, OC, and OD

are 45�, 90�, and 135� with respect to the loading directionof the upper sheet, respectively. Note that some portionnear the central hole of the spot friction weld was removedduring the cross sectioning and polishing processes. In thedirection of OB, a small fatigue crack, marked as crack 2*,emanates from the bend surface, marked as B2*. In the

direction of OC, a fatigue crack, marked as crack a*, ema-nates from the original crack tip and propagates along thezigzag interfacial surfaces into the stir zone. In the direc-tion of OD, a small fatigue crack, marked as crack 1*, ema-nates from the original crack tip. Note that small fatiguecracks 1* and 2* in Fig. 12(b) represent the extensions offatigue cracks 1 and 2 in Fig. 12(a) growing toward thewidth direction of the specimen, respectively. Fatigue cracka* in the direction of OC in this case grows mostly underdominant mode III conditions and may represent the tran-sition crack from the kinked crack 1*.

Fig. 13(a) shows a failed lap-shear specimen with a spotfriction weld made by the concave tool at the fatigue life ofnearly 105. The so-called ‘‘eyebrow crack’’ failure mode canbe seen in Fig. 13(a). Fig. 13(b) shows a top close-up viewof a spot friction weld of the failed specimen. As shown inFig. 13(b), one large fatigue crack can be seen along theright portion of the outer circumference of the weld. This

Fig. 13. (a) A failed spot friction weld lap-shear specimen made by the concave tool at the fatigue life of nearly 105, (b) a top view of a spot friction weldon the upper sheet of the failed specimen, (c) a bottom view of a spot friction weld on the lower sheet of the failed specimen, (d) a scanning electronmicrograph of the fracture surface of fatigue crack 2 as shown in Fig. 12(a), and (e) a close-up scanning electron micrograph of region I.

Leg 2

Leg 1

Stir zoneCrack 2

Crack 1

Fig. 14. A schematic of the cross section near the spot friction weld madeby the concave tool under an applied load (shown as bold arrows).


large fatigue crack is due to the growth of fatigue crack 2 asshown in Fig. 12(a). Fig. 13(c) shows a bottom close-upview of a spot friction weld of the failed specimen. Asshown in the figure, another large fatigue crack can be seennear the left portion of the spot friction weld. This largefatigue crack is due to the growth of fatigue crack 1 asshown in Fig. 12(a). As shown in Figs. 13(b) and (c), fati-gue cracks 1 and 2 are transverse through cracks growingtoward the width direction of the specimen. Fig. 13(d)shows a scanning electron micrograph on the fracture sur-face due to fatigue crack 1 from another failed specimen.Fig. 13(e) shows a close-up scanning electron micrographof region I in Fig. 13(d). The bold arrows in Figs. 13(d)and (e) show the propagation directions of the macroscopicfatigue crack fronts. As shown in Fig. 13(d), the upper por-tion is the upper sheet, the middle portion is the fracturesurface of fatigue crack 1 and the lower portion is the bot-tom surface of the weld. As shown in Fig. 13(e), both fati-gue striations and tear ridges can be seen on the fracturesurface of fatigue crack 1.

5. A kinked fatigue crack growth model

In order to develop an engineering fatigue model, weidealize the three-dimensional spot friction weld problemas a two-dimensional crack problem as in Newman andDowling [16] and Lin et al. [17]. Fig. 14 shows a schematicof the cross section near the spot friction weld made by theconcave tool under a statically equivalent combined tensileand bending load. The decomposition of the lap-shear loadto four sets of loads to derive analytical stress intensity

0 5 10 15 20 25 300

0.5

1

1.5

2

2.5

3

3.5

4

W/d

FI ,

FII

FI=(KI)Wang et al. / (KI)Zhang

FII=(KII)Wang et al. / (KII)Zhang

Fig. 16. The geometric functions FI and FII or the normalized maximumglobal KI and KII solutions at the critical locations of resistance spot welds(point A and point B as shown in Fig. 2) as functions of the ratio of thespecimen width to the nugget diameter W/d based on the global stressintensity factors of Wang et al. [15].


factor solutions can be found in Lin et al. [27]. Note thatthe fatigue crack growth behaviors of spot friction weldsmade by the concave tool under loading conditions oflow-cycle fatigue and high-cycle fatigue are similar,whereas the final failure modes of these welds under load-ing conditions of low-cycle fatigue and high-cycle fatigueare different, as shown in Figs. 9 and 13. As shown inFig. 14, a kinked fatigue crack, marked as crack 1, is initi-ated from the original crack tip with a kink angle a.Another fatigue crack, marked as crack 2, is initiated fromthe bend surface of the upper sheet. As discussed earlier,the spot friction weld made by the concave tool under cyc-lic loading conditions appears to be dominated by thekinked fatigue crack 1 in the lower sheet. Note that thekink angle a of fatigue crack 1 is estimated to be 75� forthe spot friction weld under cyclic loading conditions.

Fig. 15 shows a schematic of a main crack and a kinkedcrack with the kink length a and the kink angle a. Here, KI

and KII represent the global stress intensity factors for themain crack, and kI and kII represent the local stress inten-sity factors for the kinked crack. Note that the arrows inthe figure represent the positive values of the global andlocal stress intensity factors KI, KII, kI and kII. Here, weadopt the global stress intensity factors for the main crackin lap-shear specimens based on the theoretical works ofZhang [13] and the computational results of Wang et al.[15]. The global stress intensity factors for resistance spotwelds in lap-shear specimens [13,15,27] are

KI ¼ F I

ffiffiffi3p

F

2pdffiffitp ð1Þ

KII ¼ F II

2F

pdffiffitp ð2Þ

where t is the sheet thickness, F is the applied load, and d isthe nugget diameter. Here, the geometric functions FI andFII are expressed in terms of the specimen width W, theoverlap length V, the sheet length L, the nugget diameterd, and the sheet thickness t [15,27]. Fig. 16 shows the geo-metric functions FI and FII or the normalized maximumglobal KI and KII solutions for the main crack at the criticallocations of resistance spot welds (point A and point B asshown in Fig. 2) as functions of the normalized specimenwidth W/d based on the global stress intensity factor solu-

Main crack

KI kI

kIIKII

a

α

Kinked crack

Fig. 15. A schematic of a main crack and a kinked crack with the kinklength a and the kink angle a.

tions of Wang et al. [15]. The computational results ofWang et al. [15] were obtained for L/d = 12.08, V/d = 7.36, t/d = 0.1, and m = 0.3. The solutions shown inFig. 16 are normalized by the analytical KI and KII solu-tions given by Zhang [13]. Since the stress intensity factorsolutions for the spot friction welds are not available, weuse the stress intensity factor solutions in Eqs. (1) and (2)to estimate the fatigue lives of the spot friction welds inves-tigated here.

For kinked cracks, when the kink length approaches to0, the local stress intensity factors kI and kII can beexpressed as functions of the kink angle a and the globalKI and KII for the main crack. The local (kI)0 and (kII)0

solutions are given as [19,20]

ðkIÞ0 ¼1

43 cos

a2þ cos

3a2

� �KI �

3

4sin

a2þ sin

3a2

� �KII ð3Þ

ðkIIÞ0 ¼1

4sin

a2þ sin

3a2

� �KI þ

1

4cos

a2þ 3 cos

3a2

� �KII ð4Þ

where (kI)0 and (kII)0 represent the local kI and kII solutionsfor the kink length a approaching to 0. Based on the worksof Pan and Sheppard [21], Wang et al. [18] and Wang andPan [22], the local kI and kII solutions for kinked cracksfrom resistance spot welds are functions of the normalizedkink length a/t 0. Note that we assume the total crackgrowth distance t 0 is equal to t/sina due to the kink anglea as shown in Fig. 14. Therefore, we can express the localkI and kII solutions as

kIðaÞ ¼ fI � ðkIÞ0 ð5ÞkIIðaÞ ¼ fII � ðkIIÞ0 ð6Þ

where fI and fII are again geometric functions which de-pend on the geometric parameters of lap-shear specimens,such as the nugget diameter d, the sheet thickness t, the


specimen width W, the overlap length V, the aspect ratio ofthe crack, and the location of the crack front of interest[22]. Without any available computational results for thegiven geometries of the kinked cracks and the lap-shearspecimen, we take the geometric functions for resistancespot welds from Wang and Pan [22] to estimate the localstress intensity factors for kinked cracks. Fig. 17 showsthe geometric functions fI and fII or the normalized maxi-mum local kI and kII solutions for the kinked cracks ema-nating from the critical locations of resistance spot welds(point A and point B as shown in Fig. 2) as functions ofthe normalized kink length a/t 0 based on the three-dimen-sional finite element computations and the analytic kinkedcrack solutions in Eqs. (3) and (4) with the kink anglea = 90� for W/d = 5.91, L/d = 12.08, V/d = 7.36, t/d = 0.1, and m = 0.3 [22]. Note that when the kink anglea is close to 90�, the local stress intensity factors appearnot to be affected significantly by the kink angle a [21,28]and, consequently, the fatigue life estimations are not af-fected by the choice of a significantly [28]. The local kI

and kII solutions as functions of the kink length a can beobtained from the linear interpolation between the normal-ized local kI and kII solutions shown in Fig. 17. Note thatthe local kI and kII solutions for 0.7 < a/t 0 < 1.0 are notavailable. We assume the variations of the local kI andkII solutions for 0.7 < a/t 0 < 1.0 is the same as those for0.5 < a/t 0 < 0.7.

Since the fatigue crack growth is under local combinedmode I and mode II loading conditions, an equivalentstress intensity factor, keq, can be defined as [29]

keqðaÞ ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffikIðaÞ2 þ bkIIðaÞ2

qð7Þ

where b is an empirical constant to account for the sensitiv-ity of materials to mode II loading conditions. For lack of

0

0.5

1

1.5

2

2.5

0 0.25 0.5 0.75 1

fI = (kI)Wang & Pan / (kI)0

fII = (kII)Wang & Pan / (kII)0

f I, f

II

Fig. 17. The geometric functions fI and fII or the normalized local kI andkII solutions for the kinked crack emanating from the critical locations ofresistance spot welds (point A and point B as shown in Fig. 2) as functionsof the normalized kink length a/t 0 based on the three-dimensional finiteelement analysis and the analytic kinked crack solutions in Eqs. (3) and (4)with the kink angle a = 90� [22].

any further information, we take b as 1 in this paper. Nowwe adopt the Paris law to describe the fatigue crack prop-agation

dadN¼ CðDkeqðaÞÞm ð8Þ

where N is the life or number of cycles, C and m are mate-rial constants, and Dkeq is the range of the equivalent stressintensity factor. Since the global and local stress intensityfactors discussed here are functions of the kink length a,the fatigue life of spot friction welds can be obtained byintegrating Eq. (8) as

Nf ¼1

C

Z 0:05t0

0

½DkeqðaÞ��m daþZ 0:2t0

0:05t0½DkeqðaÞ��m da

(

þ � � �Z 1t0

0:7t0½DkeqðaÞ��m da

)ð9Þ

where 0,0.05,0.2, . . . , 0.7, and 1.0 represent several valuesof the normalized kink length a/t 0 as shown in Fig. 17.We also consider a simplified model with the local stressintensity factors kI and kII for the kink length a approach-ing to 0. In this case, keq in Eq. (7) and the Paris law in Eq.(8) can now be written to be (keq)0 as

ðkeqÞ0 ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðkIÞ20 þ bðkIIÞ20

qð10Þ

and

dadN¼ CðDðkeqÞ0Þ

m ð11Þ

The fatigue life of spot friction welds can now be obtainedby integrating Eq. (11) explicitly as

Nf ¼t0

CðDðkeqÞ0Þm ð12Þ

We here consider the simplified model since the closed formsolution exists for this case and we would like to investigatethe applicability of the simplified model.

6. Fatigue life estimations

Fig. 18 shows the experimental results for spot frictionwelds made by the concave tool and the fatigue life estima-tions based on the fatigue crack growth models in Eqs. (9)and (12). The estimations are obtained from the nuggetdiameter d = 7.69 mm, the upper sheet thicknesst = 0.94 mm under the shoulder indentation, and the kinkangle a = 75� based on the micrograph shown inFig. 12(a). Here, the nugget diameter is determined basedon the location of the original crack tip. The stress intensityfactor solutions discussed in the previous section areadopted. It should be noted that the global and local stressintensity factors depend upon many geometric parameters,such as the nugget diameter, sheet thickness, kink lengthand kink angle. The stress intensity factor solutions dis-cussed in the previous section are used as approximatesolutions to estimate the fatigue lives. Since the material

103 104 105 106400

800

1200

1600

2000

2400

Life

Loa

d ra

nge

(N)

Life prediction, kI(a) and kII(a)Life prediction, (kI)0 and (kII)0

Experimental results (concave tool)

Fig. 18. Experimental results and fatigue life estimations for spot frictionwelds made by the concave tool in lap-shear specimens. Symbols representthe experimental results and various lines represent the fatigue lifeestimations based on Eq. (9) with kI(a) and kII(a) and Eq. (12) with (kI)0

and (kII)0, respectively.


constants for the Paris law for aluminum 6111-T4 are notavailable, the material constants C ¼ 1:35� 10�7 mm=cycle

ðMPaffiffiffimpÞm

and m = 2.55 for aluminum 6013-T4 [1,30] are used to esti-mate the fatigue lives.

As shown in Fig. 18, the estimated fatigue lives deter-mined from the global KI and KII solutions in Eqs. (1)and (2) and the local kI(a) and kII(a) solutions determinedfrom the values shown in Fig. 17 appear to agree well withthe experimental results. The estimated fatigue lives basedon the global KI and KII solutions and the local (kI)0 and(kII)0 solutions in Eq. (12) appear to be slightly higher thanthe experimental results.

7. Discussion

It should be emphasized that the kinked fatigue crackmodel presented earlier is approximate in nature by consid-ering that the weld geometry of the spot friction welds is dif-ferent from that of the resistance spot welds. In general,finite element computations are needed to perform to obtainthe exact stress intensity factor solutions for the exact geom-etry and loading conditions. However, the computationaleffort is quite extensive since the computations are three-dimensional in nature and the number of the cases for theloading conditions and the weld geometries due to differentprocessing parameters are quite large. Therefore, weadopted the stress intensity factor solutions for resistancespot welds of Wang et al. [15] and Wang and Pan [22] to esti-mate the fatigue lives of the spot friction welds in this paper.

Based on the experimental observations, the spot fric-tion welds show one final failure mode under low-cycleloading conditions and another final failure mode underhigh-cycle loading conditions. However, the dominate fati-gue cracks (crack 1) in the two different failure modes ema-

nate from the identical location as shown in Figs. 8 and 12.From the mechanics viewpoint, the values of the global KI

and KII solutions near the cracks extended from bothnotches N1 and N2 for the spot friction welds should beclose to those for the corresponding resistance spot welds[15,17]. However, no kinked crack emanates from the crackextended from notch N2 (see Fig. 3). If a kinked crack wereto emanate from this location, the kinked crack shouldgrow close to the direction of the maximum local kI andthe crack should propagate into the stir zone [28]. Notethat Lin et al. [5] indicated that the grains in the stir zoneare much finer than those in the thermal mechanicalaffected zone and the base metal. Therefore, the fatiguecrack growth resistance of the stir zone may be higher thanthat of the thermal-mechanical affected zone and the basemetal to prevent the kinked crack growth near the crackextended from notch N2. Therefore, fatigue crack 1 inthe lower sheet becomes the dominant kinked fatigue crackand propagates through the sheet thickness.

Fatigue cracks 2 emanate from the bend surface of theupper sheet as shown in Figs. 8 and 12. As discussed earlier,the bend is generated by the radial expansion of the uppersheet material under the shoulder indentation as shown inFig. 3(a). The radius of the bend is relatively small whichcauses a large stress concentration on the bend surfaceunder stretching conditions. Therefore, fatigue crack 2 initi-ates here. Under low-cycle loading conditions, fatigue crack2 does not seem to affect the final failure mode. Under high-cycle loading conditions, fatigue crack 1 is considered as thedominant kinked crack since the angular span of fatiguecrack 1 is larger than that of the fatigue crack 2. However,when these cracks becomes transverse through cracks, thetransverse through crack from fatigue crack 2 can becomesthe dominant crack since the absolute crack length becomeslarger due to the larger diameter of the bend. Therefore, fati-gue crack 2 plays a major role for the final failure modeunder high-cycle loading conditions.

As shown in Fig. 18, the estimated fatigue lives of spotfriction welds made by the concave tool based on the globalKI and KII solutions and the local (kI)0 and (kII)0 solutionsin Eq. (12) are higher than those based on the global KI andKII solutions and the local kI(a) and kII(a) solutions in Eq.(9). As shown in Fig. 17, when the kink length a increases,the value of the local kI(a) solutions becomes larger thanthat of the local (kI)0 solutions but the value of the localkII(a) solutions becomes less than that of the local (kII)0

solutions. On the other hand, the local kI(a) solutions arerelatively larger than the local kII(a) solutions as reportedin Wang and Pan [22]. Consequently, the local keq(a) solu-tions in Eq. (7) become larger than the local (keq)0 solutionsin Eq. (10) for all values of a. Therefore, the estimated fati-gue lives based on the global KI and KII solutions and thelocal kI(a) and kII(a) solutions in Eq. (9) are lower thanthose based on the global KI and KII solutions and the local(kI)0 and (kII)0 solutions in Eq. (12).

Note that no effort is attempted to select the materialconstants C and m in the Paris law to fit the experimental


results. Since the material constants C and m of aluminum6111-T4 are not available, the material constants C and m

of aluminum 6013-T4 are used to estimate the fatigue livesfor aluminum 6111-T4. When the material constants ofaluminum 6111-T4 are available, it is a simple exercise tocalculate the fatigue lives for the welds. For spot frictionwelds made by the concave tool, the magnitudes of theslopes of the both fatigue life estimations, which are deter-mined by the value of m, are a bit higher than that of theexperimental results as shown in Fig. 18. One possible rea-son is that the material constant m of aluminum 6111-T4 isdifferent to that of aluminum 6013-T4.

The plunge depths of the probe pin are different for thefive welds as shown in Figs. 3(a), 7(a), 8, 10(a), and 12(a).The welds were made by a spot friction welding gun ofKawasaki Robotics, USA. Due to the load-controlledwelding process, the plunge depth cannot be controlledprecisely and, consequently, the weld geometry cannot becontrolled consistently under the specified processingparameters. Note that the fatigue crack initiation andgrowth near spot friction welds in lap-shear specimensdepend upon the weld geometry. Therefore, the load-con-trolled welding process can contribute some scattering ofthe fatigue data as shown in Figs. 5 and 18 due to the var-iation of the weld geometry. Further investigations of theeffects of the weld geometry on fatigue life are needed.

8. Conclusions

Failure modes of spot friction welds made by a concavetool in lap-shear specimens of aluminum 6111-T4 sheetsare first investigated based on experimental observations.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 failure modes of the welds under quasi-static and cyclicloading conditions are quite different. Under quasi-staticloading conditions, the failure mainly starts from the neck-ing of the upper sheet outside the weld. Under cyclic load-ing conditions, the experimental observations indicate twotypes of fatigue cracks. One type initiates and grows intothe lower sheet outside the stir zone and another type initi-ates from the bend surface of the upper sheet outside theweld. The dominant fatigue cracks for the final failures ofthe welds are the kinked fatigue crack growing in the lowersheet outside the stir zone. Based on the experimentalobservations of the paths of the dominant kinked fatiguecracks, a fatigue crack growth model of Newman andDowling [16] and Lin et al. [17] is then adopted to estimatethe fatigue lives of the spot friction welds. The global stressintensity factors and the local stress intensity factors forkinked cracks of Wang et al. [15] and Wang and Pan [22]for resistance spot welds and the Paris law for crack prop-agation are used in the fatigue crack growth model. Thefatigue life estimations based on the fatigue crack growthmodel with the global and local stress intensity factors asfunctions of the kink length and the experimentally

determined kink angles agree well with the experimentalresults.

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. Nicholsonof 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.

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