Digital Image Correlation Analysis of the Deformation Behavior of Pb-free Solders at Intermediate Strain Rates*

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1 Led-free Solders Reserch Summry Digitl Imge Correltion Anlysis of the Deformtion Behvior of P-free Solders t Intermedite Strin Rtes* K.E. Yzzie, J.J. Willims, D. Kingsury, P. Perlt, H. Jing, nd N. Chwl Digitl imge correltion (DIC) is powerful tool for quntifying locl stresses nd strins. The demnd for environmentlly enign P-free solders nd the push towrd smller portle electronics will mke it more likely for solder interconnects to encounter mechnicl shock through dropping or mishndling. Thus, quntifying the strin rte ehvior of P-free solders from the qusi-sttic to the shock regime is essentil for developing relile numericl models of the mechnicl shock ehvior. In this pper we report on the use of DIC to mesure the locl strin nd strin rte occurring in the neck of Sn-3.5Ag-.7Cu specimens, t the onset of necking. Tensile tests were conducted in the rnge 1 3 s 1 3 s 1. A prmetric study ws conducted to identify the optimum DIC prmeters for the experimentl setup. The effect of microstructure, nd pplied strin rte on the locl vlues of strin nd strin rte is discussed. INTRODUCTION The drive to produce environmentlly-enign electronic pckges hs generted gret interest in P-free lloys. 1 6 The push towrd smller electronic pckges for portle electronics hs it mde it more likely tht solder joints my fil y mishndling, such s dropping during mnufcture, shipping, or use. The microstructure, creep, nd therml ftigue ehvior of P-free solders is well understood. 7 9 However, fundmentl understnding of the ehvior of P-free solders under mechnicl shock conditions is lcking. Experimentl stress-strin dt over rnge of strin rtes is needed for fundmentl understnding of mechnicl shock, s well s for inputs in reliility models. A vriety of experimentl techniques hve een developed to chrcterize the strinrte-dependent ehvior of mterils. 1 Creep nd stress relxtion ehvior cn e quntified using screwdriven mchines t very low strin rtes. Plte impct tests cn quntify mteril ehvior t the high end or impct regime. The strin rtes experienced y solders during mechnicl shock, e.g. dropping cell phone or lptop, re in n intermedite rnge etween the qusi-sttic nd dynmic regimes. A precise rnge of strin rte How would you descrie the overll significnce of this pper? This pper descries unique nd effective mens of quntifying locl strins, y high speed imging nd digitl imge correltion, during intermedite strin rte ehvior of P-free solder lloys. descrie this work to mterils science nd engineering professionl with no experience in your technicl specilty? High speed imging coupled with digitl imge correltion provides unique mens of quntifying the locl strins nd stresses during deformtion. This technique is pplied to the deformtion nd necking ehvior of Sn-sed lloys used in electronic pckging. descrie this work to lyperson? Environmentlly-enign P-free solder lloys re eing used in electronic pckging. These new lloys hve lower mechnicl shock nd drop resistnce. This reserch ims t understnding the locl mechnisms for filure of these Sn-sed lloys under intermedite strin-rte conditions, often encountered in service. for these pplictions hs not yet een estlished. A vriety of studies hve shown tht the rnge lies somewhere etween 1 1 s 1 nd 1 2 s Boyce nd Crenshw 18 hve demonstrted tht controlled strin rtes of up to 5 s 1 cn e otined using servohydrulic methods. In previous study, we hve demonstrted the fesiility of mechnicl shock loding of ulk pure Sn solder using servohydrulic lod frme. 19 A fundmentl understnding of deformtion ehvior in these mterils, t intermedite strin rnges, requires n ccurte mens of mesuring locl strins nd strin rtes. In ddition, numericl modeling requires ccurte nd relile inputs of locl strin distriutions. Locl strin nd strin rte t necking cn e used s constitutive inputs for finite element method (FEM) models. Digitl imge correltion (DIC) is stte-of-the-rt technique for computing full-field displcements, strins, nd strin rtes on smple surfce Interferometry techniques re lso cple of mesuring full field surfce strins, ut the use of grtings or lsers mke those techniques time consuming. 26,27 Alterntively, DIC only requires high contrst, high density speckle pttern pplied to the smple surfce. A high speed digitl cmer is typiclly used to cpture the evolution of deformtion. DIC mkes use of correltion lgorithm to compre successive imges of the deforming speckle pttern. The lgorithms used compute displcement field sed on locl correltion of the positions of individul speckles. The sic principle of DIC is illustrted in Figure 1. A point with intensity x is deformed y displcement field u to finl stte x. The 18 JOM July 21

2 prolem of two-dimensionl DIC is to solve for u, where the reference nd deformed imges re relted formlly δ y y* x l = Fcet Size δ = Seprtion Distnce Between Consecutive ZOls x* u y the following eqution: 22 ui (x) xi xi ui dx j i, j 1,2 x j (1) Where u i / x j re the strin components (four strins nd two displcements). The qulity of DIC depends on the cmer resolution, time steps etween imges, lighting, qulity nd size of fetures in the speckle pttern, nd correltion prmeters. 21,28 31 The most importnt correltion prmeters re the dimension of the zone (fcet), l, over which the correltion etween the reference imge nd the deformed imge is loclly pplied; nd the center-to-center distnce etween fcets, δ. l nd δ effectively define virtul strin mesh which deforms with the stochstic pttern, s shown schemticlly in Figure 1. DIC hs een used to study the locl stresses, strins, nd strin rte distriution in metllic lloys, composites, 39,4 nd iomterils. 41,42 In the microelectronics field DIC hs een used to study the strins of solder interconnects under thermomechnicl loding, drop testing of electronic ords, 48 nd mechnicl chrcteriztion of underfills. 49 To dte, DIC hs not yet een used to study the locl strin nd strin rtes t intermedite strin rtes in Snsed lloys. In this study the mechnicl ehvior of Sn-3.5Ag-.7Cu (SAC) solder ws systemticlly quntified t strin-rtes of 1 3 s 1 3 s 1. Locl vlues of strin nd strin rte were mesured t the onset of necking, in the necking region of the tensile specimen, using DIC. The first prt of the pper descries microstructurl chrcteriztion nd experimentl results of tensile tests. The second prt discusses results of DIC mesurements. See the sider for detils mterils nd experimentl procedures. RESULTS AND DISCUSSION Tensile Behvior nd Frctogrphic Anlysis The microstructures of s-cst SAC lloys fter wter quenching nd fur- c 12 Pixels 25 Pixels d Figure 1. () Principle of digitl imge correltion. A gry scle imge x is deformed y displcement fi eld u to the stte x. The principle of DIC relies on solving for u. () Virtul mesh defi ned y the region of interest length, l, nd center-to-center grid spcing, δ. In this schemtic l = δ, nd the fcets touch, ut do not overlp. When l < δ the fcets do not overlp nd the ility of DIC to correlte displcements etween consecutive imges is diminished. When l > δ the fcets overlp nd DIC cn etter correlte displcements since the overlp produces some redundncy in the locl correltions of neighoring fcets. (c) Experimentl setup for cpturing high speed video of tensile tests. (d) Imge of tensile specimen coted with speckle pttern. MATERIALS AND EXPERIMENTAL PROCEDURE Sn-3.5Ag-.7Cu (Indium Corportion, Ithc, NY, USA) ingots were used in this study. The ingots were reflowed in grphite coted luminum mold with dimensions: 1.5 cm long, 1 cm wide, nd.8 cm high. A thermocouple plced t the ottom of the solder ws used to mesure the cooling rte. The smples were heted to 2 C ove the melting point (24 C), held for 2 s, nd cooled. Fine nd corse microstructures were otined with wter quench cooling rte of 16.5 C/s nd furnce cooling rte of 1 C/ s, respectively. Microstructurl chrcteriztion ws conducted fter reflow nd cooling. The smples were polished to finl finish with.5 µm colloidl silic solution. Scnning electron microscopy (SEM) ws used to chrcterize the microstructure. Tensile specimens were mchined from section ner the ottom of the reflowed lnk, where the cooling rte ws mesured. Microstructure chrcteriztion of the tensile specimens prior to testing reveled uniform microstructure throughout the specimens. The tensile specimens hd 1 mm gge length. A detiled schemtic is ville elsewhere. 19 The speckle pttern ws pplied to the specimen surfce s follows. The specimen surfce ws gently rded with 6 grit SiC to crete uniform roughness nd then rinsed with cetone to remove surfce contminnts. The surfce ws coted with thin lyer of white mtte-finish spry pint. Blck mtte-finish spry pint ws spryed on the white se cot to crete stochstic pttern of speckles on the order of 2 µm wide, or out 4 pixels 4 pixels in re. White light sources were used to indirectly light the specimen during testing. The test setup is shown in Figure 1c with typicl imge of specimen photogrphed under these conditions shown in Figure 1d. The servohydrulic grips in this study were highly reflective. The highly reflective surfce diminished the ility of the DIC softwre to ccurtely compute displcements. To remedy this, the grips were wrpped in white tissue pper, which effectively eliminted reflections. Tensile tests were performed on servohydrulic lod frme, in displcement control, t nominl strin rtes rnging from 1 3 s 1 to 3 s 1. A high-speed cmer (Phntom, Vision Reserch, Wyne, NJ) ws used to record video of the tensile tests using frme rtes up to 4,2 frmes per second (fps). The recorded video ws then converted to 8-it tiff imges. The strin produced in the specimen during the tensile test ws nlyzed y importing the 8-it tiffs into commercilly ville digitl imge correltion softwre (ARAMIS, Trillion Qulity System, Plymouth Meeting, PA, USA). Vol. 62 No. 7 JOM 19

3 nce cooling re shown in Figure 2. The furnce cooled SAC microstructure consisted of Ag 3 Sn needles nd Cu 6 intermetllic severl micrometers in size, s shown in Figure 2. The wter quenched SAC microstructure consisted of Sn-rich dendrites nd eutectic mixture of Sn, Cu 6, nd Ag 3 Sn, s shown in Figure 2. The engineering stress-strin curves for tensile tests of furnce cooled nd wter quenched Sn-3.5Ag-.7Cu re shown in Figure 3 nd, respectively. At the highest strin rtes n oscilltory wve, cused y reflected elstic wves, ws superimposed on the stressstrin curves. In generl, ll specimens showed n increse in ultimte tensile strength (UTS) with incresing strin rte. For given strin rte, the wter quenched specimens hd greter UTS vlues thn the furnce cooled specimens. This is expected since the finer microstructure, prticulrly in the form of fine dispersion of Ag 3 Sn prticles, increses the numer of ostcles for disloction motion. Wter quenched specimens hd greter strin-to-filure thn furnce cooled specimens. This ehvior is somewht unexpected since the corser microstructures in the furnce cooled specimens would pper to result in lower yield stress nd higher ductility. Frctogrphy ws performed on the frcture surfces t the highest nd lowest strin rte using SEM. Ag- Sn needles nd Cu Sn prticles were identified using energy dispersive spectroscopy (EDS) spot scns. The frctogrphy reveled tht in the furnce cooled specimens the Ag 3 Sn needles frctured extensively nd nucleted lrge voids tht reduced the ductility of the furnce cooled specimens, s shown in Figure 4. The Cu 6 prticles were rrely found t the ottom of ductile dimples. At the higher strin rte the Ag 3 Sn needles were frctured, s shown in Figure 4. The high trixil stresses surrounding the Ag 3 Sn needles t high strin rte cused them to frcture nd nuclete voids. The frcture surfce of the wter quenched smples consisted of smll ductile dimples, most likely nucleted y the fine intermetllic Ag 3 Sn nd Cu 6 prticles or in the pure Sn regions, s shown in Stress (MP) Figure 5. The ductile dimples were more numerous in the specimen tested t the highest strin rte, s shown in Figure 5, due to the enhnced degree of stress trixility t the higher strin rte. Thus, the elongted nture of the Ag 3 Sn needles ppers to e responsile for nucletion of lrger voids tht could colesce more esily, nd resulted in lower ductility. Digitl Imge Correltion Anlysis When conducting DIC nlysis, it is importnt to minimize ny potentil rtifcts tht my rise. These include: () vrition in light intensity, from imge to imge, during deformtion () stochstic pttern tht hs too fine or too few speckles, (c) nlyzing imges seprted y very smll time steps, nd (d) very lrge or very smll vlues of l nd δ. Vrition in light intensity cn cuse the stochstic pttern to chnge in ppernce, therey reducing the ility Strin 12 1 Figure 2. () Microstructure of furnce cooled Sn-3.5Ag-.7Cu. Lrge Ag 3 Sn needles nd locky Cu 6 prticles exist in Sn mtrix. () Microstructure of wter quenched Sn-3.5Ag-.7Cu. Sn-rich dendrites re surrounded y eutectic mixture of Sn, Ag 3 Sn, nd Cu 6. Figure 3. () Stress-strin curves for tensile tests of furnce cooled Sn-3.5Ag-.7Cu conducted t strin rtes rnging from 1 3 s 1 to 3 s 1. () Stress-strin curves for tensile tests of wter quenched Sn-3.5Ag-.7Cu conducted t strin rtes rnging from 1 3 s 1 to 3 s 1. Wter quenched Sn-3.5Ag-.7Cu showed greter ductility nd higher strengths thn furnce cooled specimens. Stress (MP) Strin 2 JOM July 21

4 Figure 4. Frcture surfces of furnce cooled Sn-3.5Ag-.7Cu. () Specimen tested t 1 3 s 1. Ag 3 Sn needles nucleted lrge voids tht decresed ductility. () Specimen tested t 3 s 1. Ag 3 Sn needles re found t the ottom of ductile dimples. Arrows point to sections of Ag 3 Sn needles tht frctured. of DIC to trck chnges in the pttern. A pttern with very fine speckles my e elow the resolution of the cmer nd mke correltion difficult. A pttern with too few speckles, or strin mesh defined with lrge δ, does not provide enough points for correltion. Using smll δ effectively cretes fine strin mesh. The fine mesh is more sensitive to light intensity vritions nd locl deformtion of the speckles, therey producing noise. Very lrge l cn lso result in too much verging of the displcements. Smll time steps correspond to smll displcements which my e elow the resolution of the system nd introduce errors. In order to minimize ny rtifcts from the vriles descried ove, prmetric study ws conducted to determine n optimum time step, l, nd δ for our experimentl conditions. A test mtrix ws conducted on imges from tensile test of wter quenched Sn-3.5Ag-.7Cu conducted t strin rte of 1 s 1. The test mtrix encompssed the effects of vrying l (rnging etween 13 2 pixels) nd δ (from 5 15 pixels) on three versions of the tensile test imges. The nlyses were conducted using different time steps etween imges, t =.1 s,.4 s, nd.17 s. Figure 5. Frcture surfces of wter quenched Sn-3.5Ag-.7Cu. () Specimen tested t 1 3 s 1 showed reltively smooth surfce interspersed with ductile dimples. () Frcture surfce of test conducted t 3 s 1 ws rougher due to the higher stresses. The effect of chnging t, l, nd δ ws determined y compring tensile strin nd strin rte t the onset of necking, nd determining whether the strin nd strin rte contours corresponded to the shpe nd size of the neck in the imges. Rigid-ody displcement clirtions were lso conducted to clirte the softwre for ctul displcements. Figure 6 shows the strin nd strin rte distriution t necking for l rnging etween 13 2 pixels, δ rnging etween 5 15 pixels, nd t =.4 s. The smllest nd lrgest time steps (t =.1 s nd t =.17 s) did not produce strong correltions etween strin nd strin rte concentrtions t the onset of necking. Strin distriutions were not prticulrly sensitive to chnges in time step, l, nd δ, except for the cse of l = 15 pixels nd δ = 5 pixels. Using spcing of δ = 5 pixels effectively creted very fine strin mesh, which ws more prone to noise in the strin distriution. Strin rte distriutions for ll comintions of time step, l, nd δ proved to e more sensitive to chnges in the vriles tested. The smllest time step, t =.1 s, corresponded to displcement etween consecutive imges tht ws elow the resolution of the DIC softwre. Thus, these smll displcements introduced noise which ws redily pprent in the strin rte plots. The comintions of l nd δ tht exhiited the most vrition in strin rte were l = 15 pixels, δ = 5 pixels nd l = 2 pixels, δ = 13 pixels. These prmeters creted fcets tht overlpped y lrge mounts. Consequently, those Figure 6. Test mtrix compring the tensile strin nd strin rte distriution t necking for l rnging 13 2 pixels, δ rnging 5 15 pixels, nd t =.4 s. The optimum DIC prmeters were t =.4 s, l = 15 pixels, nd δ = 13 pixels. These prmeters represented the experimentlly oserved necking ehvior nd frcture loction most relisticlly. The inset imge shows the specimen t frcture. Arrows indicte the loction of the frcture with respect to the neck. Vol. 62 No. 7 JOM 21

5 Figure 7. () Strin nd strin rte distriutions t necking for wter quenched specimen tested t 1 3 s 1. White dotted lines indicted the gge section. A strin concentrtion is coincident with strin rte concentrtion. Arrows indicte the loction of frcture nd its reltion to the strin nd strin rte concentrtions in the neck. () Strin nd strin rte distriutions t necking for wter quenched specimen tested t 3 s 1. the loction of frcture nd its reltion to the strin nd strin rte concentrtion in the neck. The verge strin s function of pplied strin rte is shown in Figure 8. The strin in the neck incresed with pplied strin rte. Wter quenched specimens ppered to exhiit lrger vlues of strin in the neck compred to furnce cooled specimens. This my e due to erlier onset of void nucletion nd growth in the furnce cooled specimens, s descried ove. The verge strin rte s function of pplied strin rte is shown in Figure 8. Strin rte in the neck is quite close to the pplied strin rte. This is not surprising, since the mesurements were tken t the onset of necking. It would e expected tht t lter stges of necking the locl strin rtes would increse significntly. We encountered some difficulty in crrying out DIC nlysis eyond necking nd close to filure of the specimen. The lrge deformtion in the gge section tends to spll the speckle pttern, mking it difficult to conduct DIC. Nevertheless, quntifiction of locl strin nd locl strin rte t the neck ws chieved. CONCLUSIONS comintions of l nd δ were more sensitive to noise inherent in the high speed video, such s vritions in light intensity. The specimen t frcture cn e seen s n inset in Figure 6. Arrows indicte the loction of frcture with respect to the neck. Figure 6 shows tht time step of.4 s, l = 15 pixels nd δ = 13 pixels produced strin nd strin rte color contour plots tht represented the experimentlly oserved necking ehvior nd frcture loction most relisticlly. Thus, these settings were used in the DIC nlysis to compute strin nd strin rte for ll the tensile tests. DIC nlysis of the imge corresponding to the onset of necking (t ultimte tensile strength) ws conducted. Strin nd strin rte in the tensile direction were verged over the neck of the tensile specimen. This region of initil strin intensifiction corresponded to pproximtely 1/3 the length of the originl gge length for ll experiments. As further check tht the neck ws correctly locted, ech DIC nlysis ws compred to the high speed video, nd the neck identified in the imge corresponding to the frcture loction. Figure 7 nd shows the tensile strin nd strin rte contour plots produced for wter quenched specimens tested t the lowest strin rte nd highest strin rtes, respectively. The rrows indicte Locl Strin in Neck Wter Quenched.5 Furnce Cooled Applied Strin Rte (s 1 ) Tensile tests of Sn-3.5Ag-.7Cu specimens with corse nd fine microstructures were conducted over the strin rte rnge 1 3 s 1 3 s 1. Strin nd strin rte distriutions t the onset of necking were nlyzed using the digitl imge correltion. The following conclusions were drwn from the Strin Rte in Neck (s 1 ) Wter Quenched Furnce Cooled Applied Strin Rte (s 1 ) Figure 8. () Strin in the neck of the tensile specimens t UTS versus pplied strin rte. Wter quenched specimens rech lrger vlues of strin in the neck compred to furnce cooled specimens. () Strin rte in the neck of the tensile specimens t the UTS. The strin rte in the neck is equl to the pplied strin rte JOM July 21

6 experimentl results. 1. Ultimte tensile strength incresed with incresing pplied strin rte. For given strin rte, the wter quenched specimens hd greter UTS vlues thn the furnce cooled specimens. 2. Frctogrphy reveled tht the lrge Ag 3 Sn needles in the furnce cooled specimens frctured, nucleted lrge voids, nd resulted in decresed ductility. At the highest strin rte Ag 3 Sn needles frctured long their length. The fine eutectic mixture of Ag 3 Sn nd Cu 6 in wter quenched specimens nucleted finer voids nd resulted in greter ductility. At the highest strin rte the voids ecme lrger. 3. A test mtrix ws conducted on tensile test of speckle coted wter quenched specimen to compre the effect of vrious time steps, l, nd δ on the strin nd strin rte distriutions. The test mtrix showed tht the optimum DIC prmeters for this experimentl setup were t =.4 s, l = 15 pixels, nd δ = 13 pixels. 4. Tensile strin nd strin rte in the neck of the tensile specimens, t the onset of necking, incresed with the pplied strin rte. Strin in the neck increses with pplied strin rte. Strin rte in the neck ws nerly equl to the pplied strin rte for ll tests. There ws prcticlly no difference etween the strin rtes occurring in the neck for oth the furnce cooled nd wter quenched specimens. ACKNOWLEDGEMENTS The uthors re grteful for the finncil support for this work from the Ntionl Science Foundtion Division of Mterils Reserch Metls Division (Drs. Aln Ardell, Bruce McDonld, nd Hrsh Chopr, Progrm Directors).The uthors grtefully cknowledge the use of fcilities within the Center for Solid Stte Science t Arizon Stte University. References 1. N. Chwl, Int. Mter. Rev. 54 (6) (29), pp J. Glzer, J. Electron. Mter. 23 (1994), p J. Glzer, Int. Mter. Rev. 4 (2) (1995), pp M. McCormck nd S. Jin, JOM, 45 (7) (1993), pp P.R. Vinco nd D.R. Frer, JOM, 45 (7) (1993), pp W.J. Plumridge, J. of Mter. 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Bridgmn, Studies in Lrge Plstic Flow nd Frcture with Specil Emphsis on the Effects of Hydrosttic Pressure (New York: McGrw-Hill, 1952). K.E. Yzzie, grdute reserch ssistnt, J.J. Willims, ssistnt reserch scientist, D. Kingsury, lortory mnger, P. Perlt, professor, H. Jing, ssistnt professor, nd N. Chwl, professor, re with the School of Mechnicl, Aerospce, Chemicl, nd Mterils Engineering, Fulton Schools of Engineering, Arizon Stte University, Tempe, AZ Prof. Chwl cn e reched t nchwl@su.edu. Vol. 62 No. 7 JOM 23