non-empirical modeling of fatigue in lead-free solder joints: fatigue failure analysis and...

Non-Empirical Modeling of Fatigue in Lead-Free Solder Joints: Fatigue Failure Analysis andEstimation of Fracture Parameters

D. Bhate, D. Chan, G. SubbarayanSchool of Mechanical Engineering, Purdue University, West Lafayette, IN 47907-2088, USA

Phone: (765) 494-9770, Email: ganeshsgpurdue.edu

Abstract parameters and relating this to empirical rules such as the

Predicting the fatigue life of solder interconections is Coffin-Manson rule and its variants [3]. It is common

a challenge due to the complex nonlinear behavior of knowledge that this technique does not deal with the

solder alloys and the load history. Long experience with physics of the problem at hand: as such, predictions ofSn-Pb solder alloys together with empirical fatigue life fatigue life for different material and geometry systems isSn-Pbs solder alloystheCogetherawith emirale fatuelfedu not feasible unless thermal cycling tests are repeated formodels such as the Coffin-Mansongrulekhaeh edis the various electronic packages under consideration.

altenatives. However, for thecuamently popular Pb-free Solder fatigue failure is at its essence, a fatigue crackatraie. Hwvr, fo th curnl poua Pbfe vrowth r̂oblem. It iS therefore natural that a non-choice of SnAgCu solder joints, designing accelerated g

thermal cycling tests and estimating the fatigue life are empirical understanding of this problem can only resultchallenged by the significantly different creep behavior from adopting a fracture mechanics approach. Whilerelative to Sn-Pb alloys. This study is divided into two linear elastic fracture mechanics (LEFM) does provideparts: In the first part, a hybrid fatigue modeling approach approaches such as the Paris law [4] that deal with fatigueinspired by nonlinear fracture mechanics is discussed. crack growth, the assumptions made in these approachesThe hybrid fatigue model has been shown to predict the are almost always not valid for studying crack growth in

crack trajectory and fatigue life of a Sn-Pb solder solder interconnections. This is primarily due to the factinterconnection subjected to both isothermal accelerated that typical fatigue failures in solder involve large cracksthermal and anisothermal power cycling conditions. In the (relative to pad size) and large scale yielding, both ofsecond part, results of experimental characterization via which invalidate the use ofLEFM [4]. One of the reasons

fatigue testing of microelectronic packages with SnAgCu LEFM breaks down for this class of problems is becausesolder interconections subjected to anisothermal power it does not explicitly deal with the specific nature of

conditions are described. Packages of different material degradation in the vicinity of the crack. It hascyclingr r been shown that fati ue crack oro a ation iS the endgeometries were tested to study the effects of these g p p gvariations on the estimation of fatigue life. The afore result of accumulating degradation in front of the crackmentioned hybrid model relies on the estimation of two tip (a region called as the process zone) either in the formfracture parameters which are to be determined of microcracking (as seen in cementitious composites, for

experimentally. In this study, a novel technique involving example) or formation and growth of voids (as seen intracking crack fronts in solder interconections as a ductile materials including solder) [4].function of number of fatigue cycles is proposed to Nonlinear fracture mechanics, which includes, but isestimate these fracture parameters that can be then used to not limited to the critical crack tip opening angle (CTOA)model fatigue crack growth using the hybrid modeling method, the elastoplastic J-integral approach and thetechnique. cohesive zone model aproach, has attempted to address

the issues of large scale yielding and large cracks [4]. The1. Introduction cohesive zone model has emerged as a popular approach

Solder joint fatigue has been the subject of a great primarily due to the fact that it separates materialdeal of study. The reason for this is easily understood on behavior in the process zone from bulk material behavior.examining the nature of the problem: complex and non- Then, employing a fairly straightforward cohesive law tostandardized packaging geometries, variable describe material behavior in the process zone, one canenvironmental conditions that impose strong relate tractions to separations. Crack propagationthermomechanical effects and perhaps most importantly, decisions can then be made based on a predefinedthe complex creep and rate dependent viscoplastic criticality condition. Cohesive laws are fairly simple tomaterial behavior of the solder alloys themselves. The embed into a finite element model as long as one knowsdrive towards lead-free solders has only served to add the direction of crack growth a priori.more complications to this problem on account of their The concept of isolating a region in front of the crackunique creep properties [1] and microstructure [2]. tip as a region loaded with a finite cohesive stress

Despite these complexities, the microelectronic originated in the 1960s [5, 6]. Since then, (atleast five)packaging industry primarily relies on the tried and different laws have been proposed to describe thetrusted technique of imposing controlled thermal cycling behavior of material in this zone (see Brocks et.al. [7] foron electronic packages in an experimental environment, a complete review). Since the law is purelyestimating Weibull characteristic lives and shape phenomenological, there is no fundamental reason to

1]-4244-0276-X/06/$20. 00®)2006 IEEE -4-

7th. Int. Conf: on Thermal, Mechanical and Multiphysics Simulation and Experiments in Micro-Electronics and Micro-Systems, EuroSimE 2006

believe that one form of the law is superior to another. required fracture parameters for modeling. This proposedWhile attempts have been made to connect one of the method involves tracking crack fronts using the standardseveral forms of the law [8] to the universal binding law failure analysis tool of dye penetration.proposed by Smith and Ferrante [9], it is hard to believe More work in this area is likely to result in a greaterthat the connection between atomistic observation and acceptance of non-empirical modeling tools as moremacroscopic cracking is a relevant one. The lack of relevant and versatile descriptions of fatigue failure instandardization is not restricted to the definition of the microelectronics packages. The key lies in thelaw alone: dealing with mixed mode loading is another development of easy to apply and computationallyarea where several ideas have been proposed without a inexpensive failure models, and well defined proceduresreasonable way to assess them qualitatively. In fact, to estimate the required model parameters. The hope isatleast one published work [9] questions the validity of that a non-empirical approach will allow fatigue lifeseveral assumptions made when dealing with mixed mode predictions via modeling for all kinds of packagefracture. Fatigue crack growth brings about its own share geometries and materials without resorting to full scaleof differences in published literature, primarily in the thermal cycling tests. This is the broad goal of our currentnature of the unloading-reloading mechanism and in the work.law that accounts for damage accumulation.Iawthis alsouinteforestingtonotethcmuatlittlee2. Hybrid Fracture-Damage Approach for ModelingIt iS also interesting to note that little experimental FtgeFiuei odrItroncinwork has been done to meaningfully corroborate all the Tieairepin Solder ne on oshypotheses in the literature regarding cohesive zone Towasiralprorn uetas[1 popsed a nemodels. The poor availability of experimental evidence to computatna procedure base gon th insosupport cohesive zone modeling theory can perhaps be isturbanc ef atie crac owth i solderattributed to one of the biggest challenges faced by interconnections. The salient features of the modelingresearchers who work with these models: estimation of approach are presented below, details canbe found in themodel parameters. Even the most basic cohesive laws for appropriate reference.monotonic loading involve two parameters whose A disturbance measure was proposed to be indicativeestimation is essential in order to describe the law of accumulated damage locally. The condition forcompletely [7]. More sophisticated models that deal with propagation of the crack was determined as being thefatigue crack growth often need as many as four critical value of this disturbance measure. The disturbanceparameters [11]. Although several attempts have been was estimated in terms of equivalent inelastic strain,made to estimate material parameters via direct which captures deformation in ductile materials(experimental) and indirect (experimental and numerical) adequately. The expression for disturbance wasways, there is no standard technique that can do this with determined from Weibull functions as:confidence [12]. r y 7

Any engineer dealing with the problem of solder D = 1- exp_(1)fatigue is thus faced with a dilemma: while there do existKnon-empirical models based on nonlinear fracture where 4D is the equivalent inelastic strain calculated frommechanics that can be applied to the description of solder the instantaneous plastic strain and the time dependentfatigue, their practical implementation is not creep strain; 4, and z are material constants. Discussion ofstraightforward and often raises more questions than it these material constants and their determination isprovides answers. There exists however one approach to deferred to a later section.describing fatigue crack growth in solder alloys which has It was demonstrated in [13] that the exponential formbeen successfully implemented specifically to the of Eq. (1) is similar to the form proposed by de-Andresproblem of solder joint fatigue [13]. While the approach et.al. [14] in their application of cohesive zone models tois inspired by cohesive zone models and resembles them the prediction of fatigue crack growth in axially loadedin form, the implementation of the approach is more Aluminum shafts. It was further shown in [15] that thestraightforward. Additionally, to the best of our two-parameter Weibull form from which the disturbanceknowledge, this is the only approach that has been able to function in Equation (1) is derived closely resembles thesuccessfully predict experimentally observed fatigue exponential form of the Smith-Ferrante law [9] that iscrack fronts in eutectic Sn-Pb solder interconnections that among the more popular cohesive zone modeling laws inhave undergone thermal cycling. use currently.

In the first part of this paper, we discuss this particular To achieve computational efficiency, the disturbancenonlinear fracture model that incorporates the laws of state was extrapolated to advance the crack using a one-damage mechanics to describe crack propagation in solder term Taylor expansion as:interconnections. In the second part of this paper, wepreenpeliinryresults from power cycling tests D +D +0 N+- )(2

performed on three lead-free solder packages of varying n+Nnconstructions. Based on our experimental observations, weeN anN reteum rofclsofaigeiewe propose a new method for the estimation of the

at the end of n ± 1 and n iterations, respectively. D"+ and


carethe values of the disturbance parameter associatedwith N, and N, cycles. The rate of disturbance changeover a cycle (6D aNo was calculated using finitedifference derivatives. The number of cycles for crackadvance is calculated by advancing the disturbance tocritical state, that is, by determining the number of cycleswhen D,, equals to D~, a predetermined estimate forcritical damage.

Excellent fatigue life predictions (within 200 ) were Fig. 1 Packages A, B, C ofdifferent sizes selectedformade with accurate tracking of crack paths. It was also fatigue failure characterization effortsshown that the rate of damage was fairly linear tillapproximately 6500 of the crack length. Beyond this Table 1 Details of testpackagespoint, damage increased exponentially. The change in the Package Component Solder Alloy Arrayrate of damage was found to coincide with a change in Dim. (mm) Config.fracture morphology corresponding to a transition of A 3.5 x 3.5 x 0.4 Sn-3.8Ag-0.7Cu 6 x 6failure mechanism from creep fatigue to shear overload B 12x 12txSn-4.OAg-0.5Cu 2 x 2[16]. c 29x29x1I Sn-3.8Ag-0.7Cu lIIx 11I

To the best of our knowledge, this is the onlysuccessful demonstration of accurate tracking of fatigue An anisothenral powercycling tester was employed tocrack growth in solder interconnections implemented in a generate a temperature profile ranging from 0 to 100 0C.three-dimensional finite element model using nonlinear Details of this test method were described by Setty et. al.fracture-damage mechanics. While the cohesive zone [19]. The powercycling tester has been scaled-up to runmodel approach in conjunction with damage mechanics tests on upto 16 test beds at a time. The scaled-up versionhas been employed to study solder fatigue in at least two with 8 components being tested simultaneously is shownother recent publications [17, 18], the results were not as in Figure 2.comprehensive and modeling efforts were limited to two- Test results on package A were also reported in [19]dimensional approximations with no explicit tracking of including estimation of Weibull probability plots andthe fatigue crack: solder interconnection failure was characteristic life. Since the focus of this work is onmerely related to a damage measure in both cases. studying failure non-empirically, these results are not

3. Fatigue Failure Analysis repeated here. Instead, the results from failure analysis forFatigue failure in microelectronic packages is two of the three packages using dye penetration is

conventionally determined electrically: this involves described in greater detail since it is this technique thattracking resistance in a chain which connects all or some will enable estimation of material parameters. Theof the solder interconnections in the package being tested proposed methods for the estimation of this parametersunder thermal cycling. An increase in resistance above a are discussed in detail in the following section.predefined value is used to indicate failure in the package. Package AThis resistance change is casued due to growth of a crack Powercycling and thermal cycling test results forto a critical extent in an interconnection, typically the one package A were reported in [19]. A characteristic life oflocated at the corner of the package. This resistance 2368 cycles was reported for the powercycling test.monitoring technique is employed for several packages to Failure analysis results were also reported but only withdetermine failure and a Weibull probability plot isgenerated, yielding a characteristic life. While failureanalysis tools such as cross-sectioning and dye-and-pryare often used in studying failure, they are more oftenrestricted to confirmation of failure modes andmechanisms. It is not common to directly relate theseresults to the description of failure, yet there is potentiallyuseful information stored in the description of crackfronts and their variations spatially in a package as well astheir growth over an increasing number of thermalcycles.

As mentioned previously, one of the broad goals of

packages of different tpes. Towarlds this goal, three

corresponding to Figure 1 were designed for testing. Fig. 2 Current test setup ofpowercycling tester


regard to cross-sectioning and study of voids andsecondary cracking. As part of this study, one of thesepackages was immersed in red dye in a low pressureenvironment generated by a laboratory aspirator. Thepackage was pried open by flexing the board till thepackage came loose from the board. The resulting imageof the dye penetrated solder interconnections is shown inFigure 3. It was interesting to observe clear crack frontscaptured even for a package of this small size (3.5 mm x Fig. 4 Dyepenetration ofpackage B at differentfatigue3.5 mm). A strongly visible correlation was obtained life intervals: (left to right)between crack growth and distance from the central axisof the package as shown in Figure 3. The sample in estimate electrical "failure". Nonetheless, the relativeFigure 3 was removed after approximately 2800 cycles on simplicity of the package makes it very amenable tothe powercycling tester. tracking crack fronts with increasing life cycles andPackage B allows for simple finite element models to be constructed

Several package B samples were tested to three to estimate material parameters.different life cycles on the powercycling tester and this Package Cwas followed by the afore mentioned dye-and-prywas flloweby te afoe menioneddye-ad-pry Package C was designed as a test vehicle for a numberprocedure. Excellent crack growth can be observed with of t ( h al cycingsn percycli to sudy

incrasig lfeycls. n atemtiv aproah i touseof tests (isothermal cycling and powercycling) to studyincreasimg lfe cycles. An alternative approach is to use the effects of dwell times on the creep fatigue behavior of

the multiple color dye penetration technique proposed by the solder interconnections in determination of the overallHelms and Phillips [20]. This technique involves package fatigue life. Testing is in progress and results ofremoving the package after a fixed number of cycles, failure analysis will be reported later.dyeing it with a certain color and then replacing it in thethermal cycling environment for further testing. The 4. Estimation of Model Parametersprocedure is again repeated, only this time with a dye of a In the hybrid fracture-damage model proposed bydifferent color. Helms and Phillips [20] were able to show Towashiraporn et.al [13], the two material parametersthat the mixing of colors allowed one to discern different needed for the eutectic Sn-Pb solder interconections undercrack fronts corresponding to each of the interruptions in consideration were determined by Desai et.al. [21] usingtesting. This method is very useful when limited load drop data from the cyclic response of near-eutecticcomponents are available. Sn-40 wt% Pb solder obtained from Solomon [22].

Package B consists of only four solder Towashiraporn et.al. [13] showed that improved resultsinterconnections, one at each of the four corners. This could be obtained by recalculating the materialspecimen was originally intended for developing parameters so as to reflect a more rapid rise of damageconstitutive models for Sn-Ag-Cu solders and these with equivalent plastic strain in Eq. (1). Here, weresults will be published in the near future. As such they investigate the possibility of using information from thedo not allow for electrical monitoring of resistances to crack fronts in the package undergoing testing to

determine these parameters.Traditionally, experimentally determined package

N ~~~failure pertains to a failure measure for an entire solderinterconnection. The hybrid model described in the

~~~~~~~ ~~~~~previous sections pertains to damage evolution at amaterial point. Thus estimation of material parameters forthe model must result from a study of the crack front orthe damage trajectory. We describe here two approachesthat may be followed for estimating material parameterswith such information. The accuracy of these approachescan only be determined by developing finite elementmodels using material parameters determined using thetechniques described here and comparing results to thoseobserved experimentally.

The first approach relates curvature of the crack frontto number of life cvcles. This approach was first proposed

completeness. They postulate that the shape of the crackFig. 3 Dye penetration ofpackageA after 2800 cycles, front is an arc whose end points pass through the diameterComponentandboardsideshown. Crackfronts on at the center of the solder joint, and whose radius ofboard side showgoodcorrelation to distancefrom curvature changes as the crack front propagates. Crack

central axis

-4-7th. Int. Conf: on Thermal, Mechanical and Multiphysics Simulation and Experiments in Micro-Electronics and Micro-Systems, EuroSimE 2006

propagation is divided into two rates, one that propagatesthe crack to roughly half of the solder joint, and thesecond that leads to the complete separation of the joint.They assumed that the rate of change in radius of thecrack front is constant during the two phases: 12- | .

dr -1-

const...............

dt (3)*(t~-to) =Ar r= ro

In the first region,

t (-t -) (4)

In the second region, Fig. 5 Dimensions ofpackage B with solder(rf-r;) interconnections at 4 corners. Inset shows cross-section

tff-ti = (5) ofvirgin solder interconnection

The total time to failure can thus be determined as which was then used to compute the fatigue life of the

(rf -ri (r )-ro same package under powercycling. No detailed study oft-to = + (6) the crack fronts was used to derive A. Whereas one can

r2 rt possibly estimate material parameters by using the radiusWhere the subscripts 0, i andf denote initial, intermediate of crack front-inelastic dissipation relationship discussedand failure times respectively and r indicates radius of the above, this has not been the focus of the present work andcrack front at a given time t. is presented here for the sake of completeness.

The rate of change of crack front radius was then The second possible approach is to use finite elementassumed to be proportional to the rate of inelastic modeling as a tool to determine the relationship ofdissipation Was: effective inelastic strain as determined in the model to the

- crack fronts observed experimentally. For this purpose,wXX> r oc D (7) package B was selected for modeling due to its simplicity

(1- D) of construction. The details of the geometry are shown inw w (8) Figure 5. Since this work is ongoing, we only present the

= c1W,r=c2W (8) steps of the modeling approach here.

(rf -) (r - ro From experimental results such as those shown intf- to + Figure 4, we obtain a relationship describing the progress

c2W c1w of the crack front as a function of number of fatigue

1 1 A (rf _ r0 (9) cycles. We also have the exact description of the crackr +1f _ rO front for each of these fatigue cycles. In a finite element

LYci c)Jitc1 c)j setting, we recreate the experiment in a three-dimensionalmodel. We can easily extract the shear displacement

W imposed on the solder interconnection. We then apply theBy relating failure time to cycle time and further relating shear displacement to a solder interconnection withinstantaneous dissipation rate and cycle time to an appropriate constitutive behavior and study theaverage dissipation over the cycle, they obtained number distribution of the equivalent inelastic strain in theof cycles to failure as interconnection.

F(ii>1A K(r r> In general, the distribution of inelastic strain for a| | _ Iri + | - l l given shear loading will be dependent on the geometry

N LYCI C2c ) Cl C2 )] A and constitutive behavior of the solder interconnectionAW \AW (10) and the extent of crack growth. Since the exact loadingconditions are not always known (particularly for more

complicated packages), we predict variation of theThe purpose of the above derivation was to show that normalized effective inelastic strain (keyword PEEQ in

one could relate fatigue life estimates for solder ABAQUS) at a given material point in the intact regioninterconnections of identical geometry and material Of the model as a function of number of fatigue cycles.compositions subject to two different environmental The normalization is done with respect to the peak valueconditions. In [0], a fatigue life estimate from thermal Of effective inelastic strain which is calculated rightcycling was used to determine the constant A in Eq. (10), behind the crack tip as shown in Figure 6. In other words,


Crack front Intact Region Acknowledgmentscorresponding to We would like to acknowledge the support of

experimerk National Semiconductor Texas Instruments and the High.....E.... Density Packaging Users Group in making this work

Element used possible and for supplying components for testingfor calculating U osesZ effective purp

Element used for inelastic straincalculating peak PEEQ Referencesinelastic strain for aayi renormalization 1. Plumbridge, W.J., "The analysis of creep data forPEE QpeaA solder alloys," Soldering & Surface Mount

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3. Lee, W.W., Nguyen, L.T., Selvaduray, G.S., "Solderwe extract a relationship between the effective inelastic joint fatigue models: review and applicability to chipstrain ratio estimated in the finite element model and the scale packages", Microelectronics Reliability, Vol. 40,number of life cycles imposed experimentally as: No. 2 (2000), pp. 231-244

PEEQ 4. Anderson, T.L., 1995. Fracture Mechanics:- f(N) (11) Fundamentals and Applications. CRC Press, Boca

PEEQpeak Rotan, FL.

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PEEQ ;D Applied Mechanics, vol 7 (1962), pp.55-129.PC D (12) 7. Brocks, W., Comec, A., Scheider, I., "ComputationalPEEQpeak XDcr aspects of nonlinear fracture mechanics",

Eqs. (1), (11) and (12) therefore yield: Comprehensive Structural Integrity, vol. 3 (2003), pp.Eqs. (1), (11) ~~~~~~127-209

'rD = 'rD oc f(N) (13) 8. Needleman, A., "An analysis of decohesion along an

XDcr Xc [-ln(1-Dcr )]11z imperfect interface," International Journal of Fracture,This may be then used to fit 4c and z for a given Dcr vol. 42 (1990), pp. 21-40.

for several different applied tensile loads with different N 9.Rose, J.H., Smith, J., Ferrante, J., "Universal bindingvalues, energy curves for metals and bimetallic interfaces",

Physical Review Letters, Vol. 47, No. 9 (1981), pp.5. Conclusions 675-678

The disadvantages of using empirical approaches have 10. Jin, Z.-H., Sun, C.T., "Cohesive zone modeling ofbeen discussed along with a brief discussion of the interface fracture in elastic bi-materials," Engineeringnonlinear fracture mechanics approach of cohesive zone Fracture Mechanics, 2005.modeling that can be applied to studying the problem of 11. Roe, K.L., Siegmund, T., 2003. An irreversiblesolder fatigue. The issues in applying cohesive zone cohesive zone model for interface fatigue crackmodels in practice have been pointed out and use of a growth simulation. Eng. Fract. Mech. 70, 209-232.hybrid fracture-damage model has been proposed. 12. Que, N.S., "Identification of cohesive crackPreliminary testing results from powercycling tests run on fracture parameters using mathematicalthree different packages have been presented. programming", Ph.D. Thesis, 2003, The University ofSpecifically, the tracking of crack fronts as a function of South Wales, Sydneynumber of fatigue life cycles has been demonstrated. 13. Towashiraporn P., Subbarayan G.S., Desai C.S.,Finally, it has been shown how this information may be "A hybrid model for computationally efficient fatigueused to determine the material parameters needed in the fracture simulations at microelectronic assemblyhybrid model. The accuracy of this method will be interfaces", International Journal of Solids anddetermined by the accuracy of the hybrid model to predict Structures, vol. 42 (2005), pp. 4468-4483fatigue crack growth in the lead-free packages discussed 14. de-Andre's, A., Pe'rez, J.L., Ortiz, M., 1999.here using the proposed approach for estimating the Easoati fnte lmnt nlysofte-model parameters. This modeling effort will be conducted diesoaftgucrkgowhnalmumhfsas part offuture work. subjected to axial loading. Tnt. J. Solids Struct. 36,

2231-2258.

-6-7th. Int. Conf: on Thermal, Mechanical and Multiphysics Simulation and Experiments in Micro-Electronics and Micro-Systems, EuroSimE 2006

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16. Towashiraporn, P. Subbarayan, G., "A hybridfracture-damage model for computationally efficientfracture simulations in solder joints," ElectronicsPackaging Technology, 2003 5th Conference, pp. 462-469.

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19. Setty, K., Subbarayan, G., Nguyen, L.,"Powercycling Reliability, Failure Analysis andAcceleration Factors of Pb-free Solder Joints", 2005Electronic Components and Technology Conference,pp. 907-915.

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22. Solomon, H.D., "Low cycle fatigue of 60/40 solderplastic strain limited vs. displacement limited testing,"Proceedings of ASM Electronic Packaging: Mater.Process., 1987, pp. 29-47.

Towashiraporn, P. Subbarayan, G., Mcllvanie, B.,Hunter, B.C., Love, D., Sullivan, R., "Predictivereliability models through validated correlation betweenpower cycling and thermal cycling accelerated lifetests", APACK 2001 Conference on Advances inPackaging, Singapore, pp. 326-337.


non-empirical modeling of fatigue in lead-free solder joints: fatigue failure analysis and...

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