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INTRODUCTION

In the surface mounting technology (SMT) devel-oped for electronic packaging, the devices are directlysoldered to pads on both sides of a printed wiringboard (PWB). This technology allows placement ofmore surface mount components into smaller PWBareas. However, for SMT, the ability to flex and ab-sorb thermal and mechanical strains is decreased.The thermal strain is induced by the mismatch ofthermal expansion coefficient between componentsduring processing and in service. Since the solder issofter than other components, most of the cyclicstress and strain take place in the solder. Therefore,fatigue failure, especially thermally induced, low-cycle fatigue failure, is likely to occur in the solder.

There are environmental and health concerns re-garding lead contained in conventional solder mate-

rials.1 Lead-free Sn-Ag system solders are candi-dates for SMT in the next generation. Therefore,understanding of low-cycle fatigue behavior andmechanisms of the lead-free solders is necessary fordeveloping reliable SMT electronic packaging.Kariya and Otsuka2 reported that fatigue life of Sn-3.5Ag-Bi (2 mass%, 5 mass%, and 10 mass%) for atotal axial strain-controlled test was dominated bytrue fracture ductility, which can be represented bya modified Coffin-Manson relationship with ductil-ity. Solomon3 found that fatigue life of 96.5Sn/3.5Agis generally longer than that of 60Sn/40Pb solderfor total shear strain-controlled fatigue tests at35°C and 150°C. Liang et al.4 reported that grainboundaries of tin-rich phases are weak spots forcracking in low-cycle fatigue tests of 95Sn/5Ag.However, only a limited number of reports areavailable, and low-cycle fatigue characteristics andmechanisms of lead-free solders are not yet fullyunderstood.

Journal of ELECTRONIC MATERIALS, Vol. 31, No. 2, 2002 Regular Issue Paper

Low-Cycle Fatigue Behavior and Mechanisms of a Lead-FreeSolder 96.5Sn/3.5Ag

CHAOSUAN KANCHANOMAI,1 YUKIO MIYASHITA,1 andYOSHIHARU MUTOH1,2

1.—Department of Mechanical Engineering, Nagaoka University of Technology, 1603-1 Kamito-mioka, Nagaoka 940-2188, Japan. 2.—E-mail: [email protected]

Low-cycle fatigue tests of as-cast Sn-Ag eutectic solder (96.5Sn/3.5Ag) wereperformed using a noncontact strain controlled system at 20°C. The fatigue be-havior followed the Coffin-Manson equation with a fatigue-ductility exponentof 0.76. Without local deformation and stress concentration at contact pointsbetween the extensometer and the specimen surface in strain-controlled fa-tigue tests, crack initiation and propagation behavior was observed on thespecimen surface using a replication technique. After failure, the longitudinalcross sections were also examined using scanning electron microscopy (SEM).Microcracks initiated from steps at the boundary between the Sn-dendrite andthe Sn-Ag eutectic structure and cavities along the boundaries especiallyaround the Ag3Sn particles. Stage II crack propagated in mixed manner withintergranular cracks along the Sn-dendrite boundaries and transgranularcracks through the Sn-dendrites and the Sn-Ag eutectic structure. Propaga-tion of stage II cracks could be expressed by the relation of dac/dN � 4.7 �10�11[�J]1.5, where ac is the average crack length and �J is the J-integralrange. After fatigue tests, small grains were observed in Sn-dendrites near thefracture surface.

Key words: Low-cycle fatigue, crack initiation, crack propagation, smallgrain formation, lead-free solder material, 96.5Sn/3.5Ag

(Received July 16, 2001; accepted October 8, 2001)

142

In the present study, isothermal low-cycle fatiguetests of as-cast 96.5Sn/3.5Ag were performed tostudy low-cycle fatigue behavior and failure mecha-nisms. In strain-controlled fatigue tests, an exten-someter has been commonly used to measure thedisplacement. However, for soft materials, such assolders, the local deformation and stress concentra-tion can be induced around the contact point be-tween extensometer probe and specimen surface.Cracks initiate in this area, reducing specimen life.Whitelaw et al.5 indicated that failure typically oc-curred in solder specimens after several thousandcycles due to early initiation of cracks at extensome-ter knife edges. To avoid this effect, a noncontact dis-placement measurement system6 was used in astrain-controlled fatigue test of solders.

MATERIAL AND EXPERIMENTALPROCEDURES

An Sn-Ag eutectic alloy (96.5Sn/3.5Ag), which wassupplied in as-solidified form, was used in the pres-ent study. Fatigue specimens were then machinedfrom bulk material. The specimen, designed accord-ing to the ASTM recommendation,7 has a diameterof 12 mm at the two ends, a center diameter of 6mm, and a gauge length of 9 mm. In order to removelathe machining marks as well as any possibleresidual stresses from the specimen surface, thespecimen gauge lengths were electrolytically pol-ished at room temperature at 8 V DC for 3 min. in asolution of 800 mL of ethanol (80%), 140 mL of dis-tilled water, and 60 mL of perchloric acid (60%). Thespecimens were then left to age at room tempera-ture for more than 30 days. Since the homologoustemperature at room temperature is above 0.5 forall the solders studied here, this aging treatmentalso stabilized the microstructure.8

The total strain-controlled fatigue tests were per-formed by using a servohydraulic fatigue machinewith a 2 kN load cell under 55% relative humidityand a constant temperature of 20°C. A triangularwaveform with 0.001 s�1 strain rate and R � �1strain ratio was used for the fatigue tests. The cyclicloading started in tension. Fatigue failure was de-fined as 25% reduction of maximum tensile load.

In order to avoid local deformation and stress con-centration at contact points induced by the conven-tional displacement-measuring device, the digitalimage measurement system was used in the presentstrain-controlled fatigue test. With a 50-mm charge-coupled device (CCD) camera lens and 200-mmworking distance (distance between the specimenand the lens), the field of detection is approximately10 mm in the longitudinal direction of the specimen,which covered all of the total strain ranges per-formed here. The smallest displacement that thissystem can detect is 8 �m. More detail about thisnoncontact, digital-image measurement system is inRef. 6.

During the fatigue test, cracks on the surface ofthe specimen were observed by using a replication

technique. After failure, the longitudinal cross sec-tions of specimens were examined using scanningelectron microscopy (SEM).

RESULTS AND DISCUSSION

Microstructure

To reveal the microstructure, the solder wasetched with 10 g of FeCl3, 2 mL of HCl, and 100 mLof distilled water. The SEM micrographs of the Sn-Ag eutectic alloy are shown in Fig. 1. In the Sn-Ageutectic alloy, �-Sn phase is the major phase, whichcomprises over 90% by volume. The microstructureconsists of primary �-Sn dendrites (dark) and Sn-Ag eutectic structures (light). By means of the lin-ear-intercept method, the average size of �-Sn den-drites is approximately 80 �m. Some needles andparticles of Ag3Sn can be observed in Sn-Ag eutec-tic phase. These second-phase particles of Ag3Snare approximately 0.3 �m in diameter. Some Ag3Snparticles are also present in the �-Sn-rich phase;however, the content is less than those in the Sn-Ageutectic phase. Monotonic tensile tests were con-ducted at 20°C in small strain range (about 0.03%strain) with a strain rate of 10�2 s�1. The resultantmodulus of elasticity was 50 GPa, and the hardnessobtained in this study was 11.5–13 HV. The melt-ing temperature of 96.5Sn/3.5Ag is 221°C.9

Low-Cycle Fatigue Behavior and Mechanisms of a Lead-FreeSolder 96.5Sn/3.5Ag 143

Fig. 1. The SEM micrographs of Sn-Ag eutectic solder: (a) low mag-nification and (b) high magnification.

for plastic-shear strain-controlled low-cycle fatiguetests3 and axial-torsional strain-controlled low-cyclefatigue tests.4

However, the Coffin–Manson relationship re-ported by Solomon3 for 96.5Sn/3.5Ag tested in sim-ple shear with constant frequency of 0.3 Hz at 35°Chad a fatigue-ductility exponent (�) of 0.6, based on25% reduction of hysteresis load as a failure crite-rion. Kariya and Otsuka13 obtained a fatigue-ductil-ity exponent (�) of 0.5 for 96.5Sn/3.5Ag with 0.005s�1 strain rate, R � 0, and 50% reduction of load as afailure criterion. These values of the fatigue-ductil-ity exponent (�) are lower than the present result.Since the low-cycle fatigue behavior depended on anumber of parameters, e.g., failure criteria,14,15 ma-terial condition,16 and test methodology,17 the differ-ences of the fatigue behavior among the literaturecan occur. Mei et al.16 found a significant increase infatigue life of 60Sn/40Pb with a decrease of grainsize. In the present study, the average size of �-Sndendrites is approximately 80 �m, while those ofRef. 3 and 13 are 10 �m and 5 �m, respectively. Thedifferences in the fatigue-ductility exponent (�) be-tween the present work and others3,13 may resultfrom the microstructural effect. Moreover, the fa-tigue behavior is also affected by the testing fre-quency; e.g., Shi et al.18 found the fatigue-ductilityexponent (�) of 63Sn/37Pb reduced with decreasingfrequency. A constant strain rate of 0.001 s�1 wasused in the present work, so the frequency variedfrom test to test (0.025 Hz to 0.1 Hz). It is possiblethat the variation of frequency affects the outcomeof the test, i.e., number of cycles to failure. More de-tailed discussion will be given on the effect of fre-quency on fatigue behavior of Sn-Ag eutectic solderin a future work.

Fracture Mechanism

Crack Initiation

Crack initiation was observed on the surface ofthe specimen by using a replication technique. Thespecimen, tested at 1% total strain range, was se-lected for this observation. The SEM micrographs ofreplica films, which duplicated the surface morphol-ogy of the specimen tested for a variety of numbersof cycles, are shown in Fig. 3. The replica film showsa reverse image of the specimen surface; i.e., a crackis represented by a fin on the replica film. The Sn-dendrite and Sn-Ag eutectic structure are indicatedin Fig. 3a. After 100 cycles, some cracks were ob-served at the interphase boundaries between Sn-dendrites and Sn-Ag eutectic structures and thenincreased in length and depth with an increasingnumber of cycles. Most of the cracks were isolated atthis stage, although linkage to form larger crackswas observed in a few locations. A scratch in theloading direction was made on the surface of thespecimen before the fatigue test to observe grain-boundary-sliding behavior. However, no evidence ofboundary sliding could be detected.

144 Kanchanomai, Miyashita, and Mutoh

S-N Curves

The relationship between plastic-strain rangesand number of cycles to failure can be fitted to a Cof-fin–Manson relationship.10,11

(1)

where ��p is the plastic strain range, Nf is the fa-tigue life, � is the fatigue-ductility exponent, and � isthe fatigue-ductility coefficient. The Coffin–Mansonrelationships of both the apparent plastic-strainrange (�εp

apparent), obtained from the width of thehysteresis loop at zero stress, and the calculatedplastic-strain range (�εp

calculated), obtained from thedifference between total strain range and elasticstrain (��/E) are shown in Fig. 2, compared withthose of the 63Sn/37Pb solder studied previously.12

The fatigue-ductility exponent (�) and fatigue-duc-tility coefficient (�) were obtained by using the least-squares method and are summarized in Table I. Theresults for both solders obey the Coffin–Manson rela-tionship with correlation coefficients between 0.97and 0.99.

The fatigue-ductility exponents (�) for both the�εp

apparent plot and the �εpcalculated plot are the same.

These results confirm the reliability of the presentexperimental procedure. Eutectic Sn-Ag (96.5Sn/3.5Ag) has better low-cycle fatigue resistance thaneutectic Sn-Pb (63Sn/37Pb) for all of the strainranges studied here. A similar result was reported

∆ε θα

pNf =

Fig. 2. Relationships between strain range and number of cycles tofailure for 96.5Sn/3.5Ag and 63Sn/37Pb.12

Table I. Low-Cycle Fatigue-Ductility Parametersof 96.5Sn/3.5Ag and 63Sn/37Pb12

Coffin–Manson 96.5Sn/3.5Ag 63Sn/37PbRelationship � � � �

0.76 3.64 0.63 0.63

0.74 3.38 0.68 0.85∆εpcalculated

∆εpapparent


The surface topography of the replica films (Fig. 3)was observed by a laser microscope. The relation-ship between step height at the boundary betweenthe Sn-dendrite and the Ag-Sn eutectic structureand number of cycles is shown in Fig. 4. The stepheight at the boundary between area A and area Bwas less than 0.5 �m before the fatigue test, wherethe stress concentration would not be significant.With increasing number of cycles, the step height in-creased, e.g., approximately 1 �m after 200 cycles,which also increased the stress concentration at theboundary. At this stage, some cracks could be clearlyobserved along the boundary step, which behaved asa stress raiser. After 800 cycles, the step height in-creased to approximately 2.5 �m, and longer crackswere observed.

At a high homologous temperature (approxi-mately 0.6 T/Tm at 20°C for 96.5Sn/3.5Ag), the inter-phase boundaries between Sn-dendrites and Sn-Ageutectic phases, which have high surface energy,

Fig. 3. The SEM micrographs of replica films of the surface of the specimen tested at 1% ��T: (a) before test, (b) 50 cycles, (c) 100 cycles, (d)200 cycles, and (e) 800 cycles (load is in the vertical direction).

Fig. 4. The relationship between step height at the boundary be-tween Sn-dendrite and Sn-Ag eutectic phases and number of cy-cles.


serve as preferential locations for solid-state proc-esses, e.g., diffusion and phase transformations. Inthis condition, the interphase boundaries becomeweaker than the matrix; therefore, the grain bound-ary sliding can occur and is one of the primarysources of the high-temperature fracture mecha-nism. This sliding can cause intergranular fractureduring fatigue and reduce fatigue life. However, theeffect of sliding is reduced when fine-hardening par-ticles are homogeneously introduced into the grainboundary.19 For the 96.5Sn/3.5Ag solder, secondphases of Ag3Sn (in the form of particles and nee-dles) were observed along the boundary of Sn-den-drites. Moreover, the dendrite structure, similar tobranches of a fir tree, does not favor the slidingprocess due to the interlocking of many dendritearms.20 Therefore, it is not surprising that the slid-ing process is not the dominant behavior for this Pb-free solder. However, the difference in deformationbetween Sn-rich phases and Sn-Ag eutectic phasescan appear on the surface of a specimen and showthe steplike patterns along the boundaries. Similarboundary steps were systematically observed byKim and Laird,21,22 who studied the crack nucle-ation phenomena in the low-cycle fatigue of copper.

For the total strain ranges studied here, voidswere observed along the boundary of Sn-dendriteson the polished surface of the specimen, especiallyon the interphases between the Sn matrix (dark)and Ag3Sn phases (light). The void size is approxi-mately 2–3 �m. In some places, the voids coalescedand formed a crack. Evidence of voids on the pol-ished surface of the specimen, tested at 1.5% totalstrain range, is shown in Fig. 5. For a 63Sn/37Pb sol-der,12 colony boundary sliding with wedge cracks atthe triple-point corner of the colony boundary, andvoids along colony boundaries, especially on the in-terphases between Sn and Pb phases, were also ob-served in the early stage of fatigue life. Raman andReiley23,24 reported boundary microvoids for a Pb-Snsolid-solution alloy during cyclic deformation andPb-Sn interphase cavitation for eutectic Sn-Pb sol-der alloys during high-temperature fatigue. Voids atthe grain boundaries in Sn/Pb solder joints25 and a

bulk Sn/Pb solder26 were also reported. However,those studies were performed on Sn-Pb alloys withequiaxial grains, while the present work was on thePb-free solder with a dendrite structure.

Crack Propagation

Many crack initiation sites are available in thepresent material, so multiple cracks formed duringthe low-cycle fatigue tests. With an increasing num-ber of cycles, the number of multiple cracks on thesurface of the specimen increased; however, theirsize was limited to the size of the Sn-dendriteboundaries. Growth of these multiple cracks into thesolder was also limited (approximately 5–10 �m), sothe multiple cracks were “shallow surface cracks.”An example of a surface crack (arrow) is shown inFig. 6. After a certain number of cycles, some of thesurface cracks eventually link-up to form largercracks. The link-up process was mixed manner, i.e.,intergranular along Sn-dendrite boundaries andtransgranular through the Sn-dendrites and the Sn-Ag eutectic phases.

Since the Sn-Ag eutectic phase, i.e., pure Sn withAg3Sn intermetallic particles, has higher strength(approximately 13 HV) than that of the Sn-dendritephase (approximately 11.5 HV), the linked cracks(approximately 20–50 �m in depth direction) areusually arrested at the boundary of the Sn-Ag eutec-tic phase, as shown in Fig. 7. However, some of thelinked cracks propagate longer for both the surfaceand depth direction of the specimen. At this stage,long linked cracks (more than 1 mm) can be ob-served on the surface of the specimen, as shown inFig. 8. The transition from linkup to propagation canbe indicated from the reduction in nominal stresswith increasing numbers of cycles. A relationshipbetween nominal stress and number of cycles for thespecimen tested at 1% total strain range is shown inFig. 9. Rapidly reduced stress levels due to the initi-ation and link-up of multiple surface cracks, can beobserved in the beginning of the fatigue test (lessthan 0.2 N/Nf or 800 cycles), while the stress reducesmore slowly due to the propagation of cracks insidethe specimen is observed in the following stage. In

Fig. 5. The SEM micrograph of voids observed on the polished-sur-face of the specimen tested at 1.5% ��T (load is in the vertical di-rection).

Fig. 6. The SEM micrograph of surface crack on the longitudinalcross section of the specimen tested at 1% ��T (load is in the verti-cal direction).


this stage, other factors, such as recrystallizationand strain localization, may also contribute to thereduction of the resultant stress. However, the crackpropagation, which simultaneously reduces theload-bearing area, is presumably the dominatingmechanism for the reduction of stress. The propaga-tion process, as shown in Fig. 10, was also mixedmanner, i.e., intergranular along Sn-dendriteboundaries and transgranular manner through theSn-dendrites and Sn-Ag eutectic phases.

Once macroscopic cracks started to propagate in-side the specimen, the cracking area increased with

propagation of these cracks. Therefore, the load,which was required for maintaining a constant totalstrain range, decreased with increasing number ofcycles. The pattern of load reduction can be de-scribed by a load-drop parameter. This parameter isrepresented in the following equation:

(2)

where φ is the load-drop parameter, �P is the loadrange, and �Pm is the maximum load range. Themaximum load range was observed at the beginningof each test. The relationship between the load-dropparameter and the number of cycles for different ��Tis shown in Fig. 11. The load-drop parameter curvescan be divided into three stages: an initial rapid in-crease stage, a steady-state stage, and a final acceler-ation stage. The steady state dominates the fatiguelife. Therefore, the slope of the load-drop parametercurve in the steady state reflects the low-cycle fatiguelife; the fatigue life is longer with a flatter slope in thesteady state. The similar pattern of load-drop param-eter curves for a uniaxial fatigue test was observed by

φ = −1 ( / )∆ ∆P Pm

Fig. 7. The SEM micrograph of the arrested link-up crack observedon the longitudinal cross section of the failed specimen tested at 1%��T (load is in the vertical direction).

Fig. 8. The SEM micrographs of the replica films of the surface ofthe specimen tested at 800 cycles, 1% ��T: (a) low magnificationand (b) high magnification (load is in the vertical direction).

Fig. 9. The relationship between maximum nominal stress andnumber of cycles for specimen tested at 1% ��T.

Fig. 10. The SEM micrograph of the longitudinal cross section ofthe specimen tested at 1% ��T: intergranular along Sn-dendriteboundaries (arrow A), transgranular through Sn-dendrites (arrow B),and transgranular through Sn-Ag eutectic phases (arrow C) (load isin the vertical direction).


Kariya and Otsuka2 for an Sn/3.5Ag/5In solder andJiang et al.27 for an Sn-Pb eutectic solder. They pro-posed that the load-drop parameter could be corre-lated with an increase in the cracking area. The cor-relation of the drop in load with the cracking areawas done qualitatively with the aid of an ultrasonicmicroscopy investigation during shear-loading fa-tigue tests by Solomon.17 The correlation was also in-vestigated by Guo et al.,28 where the shear-loadingfatigue specimens were fractured in liquid nitrogento measure the fatigue-cracking area and comparedwith the load-drop parameter. They indicated thatthe growth of crack could be identified with thesteady state in the plot of load-drop parameter () vs.number of cycles (N). As the first order of approxima-tion, the relationship between the load-drop parame-ter and the cracking area can be expressed by the fol-lowing equation:

(3)

where Ac is the cracking area and A0 is the nominalcross-sectional area. The load range decreases withincreasing the cracking area. Since a number ofcracks were formed and then linked-up around thespecimen, the assumption of a circumferential crackwas made in the present study. The schematic ofcracking area (Ac) and average crack length (ac) fora linked-up circumferential crack is shown in Fig.12. The relationship between cracking area (Ac) andaverage crack length (ac) can be given as

(4)

where r is the radius of the cross section of the spec-imen. In the crack-growth stage, crack-growth rates(dac/dN) can be estimated by using Eqs. 3 and 4 andthe load-drop parameter curve shown in Fig. 11.

Since the present fatigue tests were performed inthe fully plastic region, the stress distributed uni-formly along the uncracked portion of the specimen.The magnitudes of the uniform stresses were approx-imately equal to the yield strength. For a fully plastic

A a 2r ac c c= −π ( )

1 − =( / )∆ ∆P P A /Am 0c

case, the J-integral can be used to represent the in-tensity of the elasto-plastic stress and strain fieldaround the crack tip. However, the J-integral may be-come path dependent and depend on the integrationcontour size for a material in which cavities nucleateand grow, if fracture occurs after large material soft-ening due to void nucleation and growth.29 For thepresent work, voids were mostly observed aroundAg3Sn particles, which located along the boundary ofSn-dendrites, while none of them could be observed inSn-rich phases (comprises over 90% by volume).Since the volume fraction of void was low and evenless during the nucleate and growth stage, the largematerial softening due to void nucleation and growthwould not be possible. Therefore, the J-integral couldbe effectively used for the present condition.

The J-integral was estimated by using the simpli-fied J-evaluation method, proposed by Miura et al.30

and Shimakawa et al.:31

(5)

where �J is the J-integral range; U is the crack-opening ratio, which is set to unity for the fully plas-tic case; F is the plastic-correction factor; and Je isthe elastic J-integral. The value of the plastic-cor-rection factor (F) can be determined as follows:

(6)

(7)

(8)

where �ref is the reference strain, which correspondsto the reference stress (�ref) in cyclic stress-strainhysteresis loop; and the plastic-collapse load is theload that corresponds to the yield stress.

Although a circumferential crack in the presentstudy is rather shallow, with approximately 400 �mdepth, Poisson contraction in the lateral directioncould not freely occur around the crack tip, and the

Yield stress Ligament area= ×

Plastic collapse load

σ ref = ×Applied loadPlastic collapse load

Yield stress

F E= ε σref ref/

∆J U FJ2e= 4

Fig. 11. The relationship between load-drop parameter and numberof cycles for different ��T.

Fig. 12. Schematic illustration of cracking area (Ac) and averagecrack length (ac) for a circumferential crack.


state of strain is close to the case of plane strain. Asa first order of approximation, the elastic J-integral(Je) can be determined as follows:

(9)

where E is the Young’s modulus; is the Poisson’sratio, which is 0.39 for eutectic Sn-Ag solder; and KIis the mode I stress-intensity factor range. For thecase of a round bar with a circumferential crack, KIcan be given as32

(10)

where F2 is the geometry function, and �net is thenet-section stress, taking into account the crackingarea. Since crack opening occurs only in the tensileportion of the cycle, it can be assumed that only thetensile-loading part influences the crack-growth be-havior. A relationship between dac/dN and �J atvarious total strain ranges in the steady state isshown in Fig. 13. The crack-growth curve can be rep-resented by the following equation:

(11)

where the values of C and n are 4.7 � 10�11 and1.5, respectively. Previous fatigue crack-growthtest results,33 using a compact-tension (CT) speci-men under a stress ratio of 0.1, a frequency of 0.1Hz, and a constant temperature of 20°C, is com-pared with the present result, as shown in Fig. 13.As can be seen from this figure, the fatigue crack-growth curve obtained by using a round-bar speci-men under a low-cycle fatigue condition correlateswell with that obtained by using a CT specimenunder a high-cycle fatigue condition.

Evidence of a boundary step and the cavitiesalong Sn-dendrite boundaries is available, so it isexpected that specimens would fail by the accumu-lation of damage due to creep-fatigue interaction. Inthe time-dependent regime, the parameter, C*, cancharacterize the crack-growth behavior. More de-

da dN C( J)cn/ = ∆

K a F r a rI c 2 c= −σ πnet ( )

J K (1 ) Ee I2 2= − ν

tailed discussion will be given on the relationshipbetween dac/dt and C* in a future work.

Microstructural Instability

On the longitudinal cross section of the tested spec-imen, small grains (approximately 5–20 �m) were ob-served mostly in the Sn-dendrite phases in the regionnear the fracture surface. Evidence of these smallgrains is shown in Fig. 14, which should be comparedwith Fig. 1, where small grains cannot be found.Large amounts of strain energy (in the form of dislo-cation) must be induced in the large strain regionnear the fracture surface. The strain energy in thesolder may be released by recrystallizing into newstrain-free grains, or by rearranging the dislocationinto low-strain energy subgrains or substructures.

Fig. 13. The relationship between dac/dN and �J in the steadystate.

Fig. 14. Small grains observed on the longitudinal cross section ofthe specimen tested at 2% ��T: (a) location of observation, (b) SEMmicrograph observed in area A, and (c) SEM micrograph observedin area B (load is in the vertical direction).


Recrystallization involves a diffusion process, whichusually occurs in low stacking-fault energy materialsunder high-temperature conditions, while dislocationrearrangement (sometimes called polygonization) in-volves dislocation movement, which usually occurs inhigh stacking-fault energy materials under high dis-location-density condition. Hardwick et al.34 indi-cated that subgrains usually form in metals thathave high stacking-fault energies, e.g., tin. The sub-grains in Sn-rich phase were also observed for thecreep test of pure tin35 and low-cycle fatigue test of63Sn/37Pb.12 Moreover, change in phase distribution(phase coarsing), which is common behavior for therecrystallization process, could not be observed in thespecimens tested. Therefore, the small grains ob-served in this study probably resulted from polygoni-zation rather than recrystallization.

CONCLUSIONS

Isothermal low-cycle fatigue tests of a Pb-free(96.5Sn/3.5Ag) solder material have been carriedout using a noncontact strain-controlled fatigue testsystem at a constant temperature of 20°C. The mainconclusions obtained are summarized as follows.

• The low-cycle fatigue behavior of Sn-Ag eutectic(96.5Sn/3.5Ag) solder followed the Coffin-Man-son equation with a fatigue-ductility exponentof 0.76. The 96.5Sn/3.5Ag solder has a higherlow-cycle fatigue resistance than the 63Sn/37Pbsolder.12

• Boundary steps and microcracks along Sn-den-drite boundaries were observed in the earlystage of fatigue life. The crack-initiation siteswere both the boundary step and the cavities(approximately 2–3 �m) along the Sn-dendriteboundaries, especially on the interphases be-tween the Sn matrix and Ag3Sn phases.

• Multiple surface cracks initiated in an intergran-ular manner along the Sn-dendrite boundaries.After a certain number of fatigue cycles, the mul-tiple cracks linked-up to form macroscopiccracks, which propagated inside the specimen inmixed manner, i.e., intergranular along Sn-den-drite boundaries and transgranular through Sn-dendrites and Sn-Ag eutectic phases.

• The relationship between a load-drop parame-ter and the number of cycles could be dividedinto three stages: initial rapid increase stage,steady-state stage, and final acceleration stage.The steady state dominated the fatigue life. Theslope of the load-drop parameter curve in thesteady stage corresponded to low-cycle fatiguelife; the fatigue life became longer as the slopebecame flatter.

• Based on the assumption of a circumferentialcrack, a relationship between dac/dN, whichwas estimated from the load-drop parameter

curve in the steady state, and DJ, which was es-timated by a simplified J-evaluation method,was obtained. The fatigue crack-growth curvecorrelated well with the reported fatigue crack-growth test result using a CT specimen.33

• After the fatigue tests, small grains (approxi-mately 5–20 �m) were observed along the frac-ture surface (mostly in the Sn-dendrites). Dislo-cation rearrangement (polygonization) is specu-lated to be the cause of this small grain forma-tion.

ACKNOWLEDGEMENT

The authors thank T. Ori, Oki Electric IndustryCo., Ltd., for supplying the solder materials used inthis work.

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