Computational Materials Science 45 (2009) 576–583

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Computational Materials Science

journal homepage: www.elsevier .com/locate/commatsci

Fracture mechanics analysis of solder joint intermetallic compounds in shear test

M.O. Alam a,*, H. Lu a, Chris Bailey a, Y.C. Chan b

a School of Computing and Mathematical Sciences, University of Greenwich, 30 Park Row, London SE10, 9LS, UKb Department of Electronic Engineering, City University of Hong Kong, 83, Tat Chee Avenue, Kowloon Tong, Hong Kong, China

a r t i c l e i n f o

Article history:Received 24 October 2008Received in revised form 22 November 2008Accepted 2 December 2008Available online 21 January 2009

Keywords:SolderIntermetallicPb-freeBGAElectronic packageStress intensity factorPlastic deformationButt joints

0927-0256/$ - see front matter Crown Copyright � 2doi:10.1016/j.commatsci.2008.12.001

* Corresponding author. Tel.: +44 1235510165; faxE-mail addresses: M.O.Alam@gre.ac.uk, ohidul.alam

a b s t r a c t

Solder joints in the electronics products are considered as critical reliability concerns. In this research, aquantitative evaluation of fracture mechanics parameters (such as Stress intensity factors (SIF, KI and KII)and kink angle, h) in the IMC layer for SnPb and Pb-free solder joints has been carried out. Computationmethods are based on finite element numerical modelling of stress analysis in a copper-IMC-solder-IMC-copper assembly under shearing condition. It is assumed that only one crack is present in one of the IMClayers. Linear Elastic Fracture Mechanics (LEFM) approach is used for the parametric study of SIFs and h,at the predefined crack in the IMC layer of solder butt joint shear sample.

Among different parameters studied in this research, the location of the crack from the solder interfaceshas been found to be very sensitive. Crack near 1 micron distance from the interface has been found to bevery prone to propagate. It is interesting to see that a thicker IMC layer reduces crack propagation pro-pensity if there is only a single crack exists in the IMC layer and that crack is located at the middle of theIMC layer. Even if the whole solder layer is replaced by the IMC in the solder joint, the fracture propaga-tion possibility is greatly reduced. Thickness of solder joints is also found to have a significant influenceon the SIF values. It has been found that soft solder matrix generates non-uniform plastic deformationacross the solder-IMC interface near the crack tip that is responsible to obtain a wide range of KI, KII

and h values.Crown Copyright � 2008 Published by Elsevier B.V. All rights reserved.

1. Introduction

The solder alloy is a very complex material having deformationcharacteristics of elastic, plastic, creep, viscoelastic and viscoplasticmodes. Yet, when it forms joints with the substrate material of dif-ferent metals or alloys new complexities arise because of the for-mation of intermetallic compound (IMCs) at the solder jointinterface. Typically, a Cu substrate is used as a wettable metalliza-tion pad in electronic soldering applications. At the Cu/solder inter-face, Sn reacts rapidly with Cu to form Cu6Sn5 IMC during reflowsoldering. The typically morphology of IMCs at the substrate/solderinterface is a thin layer along with IMC spikes perpendicular to theIMC layer. However, the layer type IMC grows over the subsequentaging period [1–4].

It has been reported that the strength of the solder joint de-creases with an increasing thickness of IMCs formed at the inter-face and therefore, the IMC has been believed as an initiation sitefor microcracks [5–8]. Depending on the IMC thickness and differ-ent layers of IMCs at the interface as well as the location of the firstcritical crack, the fracture propagates either through the IMC layersor it switches from IMC to solder and again solder to IMC [6–8]. In

008 Published by Elsevier B.V. All

: +44 2083318665.@gmail.com (M.O. Alam).

fact, a stress singularity might always exist at the interface of IMCand solder due to asymmetry in their elastic and plastic properties.This stress singularity tends to exhibit higher stress intensity fac-tors (SIFs) and mode mixity at the tip of a crack in the IMC layerat the solder joint interface as compared to the equivalent crackin homogenous materials.

The stress singularity and fracture initiation criterion of bondedjoints of brittle and ductile materials at their interface has been thesubject of extensive theoretical and experimental investigation forthe last few decays [9–12]. Investigations into cracking near theinterface of ceramic-metal bonding reveals that cracks in the cera-mic region deflected towards the ductile metal layer, however,they switch back again to brittle layer forming a jig-jag fracturepath similar to that observed at the solder interface. Fracturemechanics approach was used for those theoretical studies. Anin-depth understanding of the fracture path at the solder interfacedemands similar approach. Moreover, because of the viscoplasticproperties of solder alloys, cracks inside the IMC layer experiencecomplicated compliance mismatch dependent stress concentrationthat were not studied much quantitatively.

Generally the shear test, as shown in Fig. 1, is conducted tostudy reliability of Ball Grid Array (BGA) solder joints. In our exper-imental work, we have carried out extensive shear strength mea-surement of BGA solder joints for different pad metallization and

rights reserved.

IMC

Solder maskNi

Solder mask Cu Pad

Substrate

Shear Ram

Solder

Fig. 1. Schematic diagram of the shear test configuration for a solder joint.

M.O. Alam et al. / Computational Materials Science 45 (2009) 576–583 577

for different aging periods [2–4]. Fracture morphology has alsobeen studied where IMC layer was found to play a significant role.Complete brittle fractures as well as ductile-brittle fractures at thesolder interface have been revealed (see Fig. 2). Shear strength val-ues of the solder joints have been found to be in the range of10 MPa to 25 MPa depending on the fracture modes. Most brittlefractures have been occurred within 10–12 MPa of shear strengthand also propagated through the IMC layer (see Fig. 2a and b).

Solder joint modelling has been attracted a great deal of atten-tion over the last three decays as they are found vital in the reli-ability prediction of electronic products. Finite element tools arewidely used in the electronic industry for rapid design optimiza-tion during the product development phase as well as failure anal-ysis of product returned from the field. Solder joints are usuallymodelled as a homogeneous and isotropic without consideringIMCs. Whereas, the IMC layer at the solder interface is consideredas the crack initiation sites [5–8].

Fig. 2. Examples of solder interface fracture through the IMC layer and IMC-solder laypropagate through the IMC layer (a and b). Different extent of ductile-brittle fracture is

The primary objective of this research is to provide quantitativeevaluation of fracture mechanics properties such as Stress intensityfactors (SIF, KI and KII) and kink angle, h, in the IMC layer for SnPband Pb-free solder joints in shear loading conditions. However, in-stead of using the BGA solder joint model, a simple model is usedthat is similar to a tensile butt joints model previously carried out[13]. A comparison is also carried out to reveal how solder materi-als behave under tensile loading and shear loading.

2. Numerical method

2.1. Model for finite element analysis

The test configuration for shear consists of two plates of Cusandwiched by a solder alloy as depicted in Fig. 3. To simulate/compare with the typical Ball Grid Array (BGA) solder joint, shearload is applied at the one side of the top Cu plate while the bottomCu plate is kept fixed from the opposite side. A tensile specimen ofa butt joint of the solder alloy sandwiched between two copperplates is also considered to compare with the shear loading. It is as-sumed that 2–20 lm thick IMC layers are formed at the solder-copper substrate interfaces. Therefore, four parallel interfaces suchas a copper-IMC, an IMC-solder, a solder-IMC and an IMC-copperare available in the specimen as shown in Fig. 3. A crack of10 lm depth from the left edge and parallel to the interface is con-sidered to be situated within one of the IMC layer. It is worth men-tioning here that, for the sake of simplicity, only one crack of10 lm in length was considered in this study while real solderjoints might contains more cracks with different sizes. Locationof the crack from the interface is varied from 1 lm to 10 lm. Thick-ness of the solder layer is also varied from 0.3 mm to 1 mm. Spec-imens are modelled in 2-dimensions under plain strain conditions.Finite element analysis has been conducted using a commercial FEsoftware package, ANSYS-11.

er. Complete brittle fracture without any deformation is noticeable while fractureusually seen while fracture propagates through IMC and solder (c and d).

Fig. 3. Model of IMC crack at the IMC-solder interface of shear butt-joint solder sample.

Table 1Material properties of Cu and IMC.

Materials Elastic modulus, E (Pa) Poisson’ ration, t

Cu 128.7 � 109 0.34IMC 85 � 109 0.31SAC 48 � 109 0.4SnPb 29.8 � 109 0.4

Table 2The values of the Anand’s constant for SnPb and SnAgCu solder used for this study.

Ansysconstant

Materialsparameters

Definition SnPb SnAgCu

1 so Initial value of deformationresistance

56.33 39.09

2 Q/k (1/K) Activation Energy/Boltzmann’sconstant

10830 8930

3 A (1/s) Pre-exponential factor 1.49e7 2.23e44 n Multiplier of stress 11 65 m Stain rate sensitivity of stress 0.303 0.1826 ho(psi) Hardening constant 2640.75 3321.157 s^(psi) Coefficient for deformation

resistance saturation value80.42 1,73.81

8 n Strain rate sensitivity of saturation(deformation resistance) value

0.023 0.018

9 a Strain rate sensitivity of hardening 1.34 1.82

578 M.O. Alam et al. / Computational Materials Science 45 (2009) 576–583

2.2. Material model

In the computational model, Cu and IMC layer are considered tobe isotropic linear elastic, whereas the solder material is consid-ered to be a viscoplastic material. Table 1 lists material propertiesof Cu, IMC, Pb-free SnAgCu (SAC) and SnPb used in the FEManalysis.

To capture the viscoplastic material model of the solder alloys,an ANAND model has been used through ANSYS finite elementcode. Previously, a specific viscoplastic constitutive law was neededto define as a user-defined subroutine code to represent the non-linear rate dependent stress-strain relations in some finite elementprograms, however, recent versions of ANSYS incorporated a well-accepted rate dependent phenomenological model that was firstproposed by Anand. That Anand’s constitutive model considerslarge isotropic viscoplastic deformations but small elastic deforma-tions. There are two main features in Anand model [14–15]:

1. no explicit yield condition and no loading/unloading criterion2. a single scalar, the deformation resistance, s, is employed as an

internal variable to represent the averaged isotropic resistanceto macroscopic plastic flow arose from strengthening mecha-nism such as dislocation filing up etc.

The values of the Anand’s constant for SnPb and SAC solder pre-sented in Table 2 were extracted from Ref. [15] for this research.The solder joint part of the butt-joint sample was meshed usingthe viscoplastic element of ANSYS, VISCO108, along with the val-ues of materials parameters of Anand’s constant.

2.3. Numerical methods for stress intensity factor evaluation

Stress intensity factors (SIFs) such as KI (for tensile mode) andKII (for shear mode) play a major role in linear elastic fracture

mechanics (LEFM) analyses. Many numerical methods using finiteelement analysis have been developed to obtain the SIFs along apre-existing crack front. The most common method of SIF calcula-tion is the extrapolation of the displacements in the vicinity of thecrack tip and uses the analytical expressions given by the LEFM[16]. Ansys v.11’s LEFM fracture mechanics macro was used tocompute SIFs for this work.

As the stresses and strains are singular at the crack tip, varyingas 1/r1/2, singular finite elements with the mid-side nodes shiftedto the quarter-point introduced by Barsoum are usually adaptedin the FEA to improve the numerical results in the vicinity of thecrack tip [17]. Elements are initially generated circumferentiallyabout, and radially away from the keypoint (i.e., the crack tip) asshown in Fig. 3.

The stress intensity factor associated with the fracture tough-ness of the material is called the critical stress intensity factor KC,where KC is material dependent. KC of a material can be obtainedonly by experiment. It is commonly used to compare with thestructural SIF to determine the critical load as well as the criticalcrack size (In any engineering design, K should not exceed thanKC). Therefore, in this work, we have used KC of IMC reported fromother experimental scientists to compare with our computed SIFvalues.

2

2.5

3

3.5

4

, MP

a-m

0.5

KI-near to SACKII-near to SACKI-near to SnPbKII-near to SnPbKI - no solder-only IMCK - criticalKII - no solder-only IMC

M.O. Alam et al. / Computational Materials Science 45 (2009) 576–583 579

3. Results and discussion

Fig. 4 compares the localization/extend of highly deformationregion at the butt-joint of solder alloy under (a) tensile and (b)shear loading. In this research, the location of the crack is assumedto be in the left edge of the lower IMC layer (see Fig. 3). Therefore,it is clear from the Fig. 4b that the solder region near the crack ex-erts relatively higher strain. However, keeping the same geometry

Fig. 4. Comparison of the localization/extent of highly deformation region at thebutt-joint of solder alloy under (a) tensile and (b) shear loading.

0

0.5

1

1.5

0 5 10 15 20Applied Loading (Stress, MPa)

SIF

Fig. 5. Variation in SIF values of solder joint shear test samples of Pb-free (SAC), andSnPb solders and a joint where solder material is replaced by the IMC with theapplied loading (solder layer thickness is 1mm, position of the crack is 2 lm awayfrom the IMC-solder interface, and loading rate is 0.8 MPa/s).

and loading conditions, the present study focuses on how fracturemechanic properties (such as KI, KII and h values) varied with:

1. Alloys composition, i.e., materials properties of solder alloys,2. Loading, i.e. applied stress,3. Location of the crack in the IMC layer, i.e., distance from the

IMC-solder interface,4. Solder joint thickness, i.e. volume of the solder materials within

the joint.

The effect of all these factors are described as follows where it isseen that distance from the interface has been found to be muchmore sensitive. While Ref. [13] describes the results of tensilebutt-solder joints, this paper concentrates in shear butt-solderjoints.

3.1. Effect of applied stress

Fig. 5 compares SIF values of the IMC layers of the solder butt-joint shear test samples with the joint where the solder material isreplaced by the elastic IMC material. A constant loading rate(0.8 MPa/s) was used within the loading range of 6–20 MPa at25 �C while the joint thickness was �1 mm. The location of thecrack was 1lm away from the solder-IMC interface. Along withthe applied stress, location of the crack position from the solderinterface and solder thickness were also found to have significanteffect on SIF values that will be described in the following sections.The curves in Fig. 5 also compare the relationship between SIFs (KI

and KII) for SAC and SnPb solder. In a shear butt-joint sample of sol-der joints where the solder material is replaced by IMC, KI and KII

values increase linearly with the applied load, whilst, the presenceof solder alloys have made significant changes in SIF values – KI

and KII values increases abruptly and shows peak/hump around10–12 MPa. This peak/hump in the SIF values is believed to bethe presence of highly viscoelastic solder materials compared tocomparatively rigid IMC materials. Due to lower values of elasticmodulus (E) of solder alloys, the local stress/strain distributionnear the crack tip at the solder-IMC interface increases which inturn is responsible for higher SIF values. As the E value of SnPb sol-der is bit lower, we see a little higher value of SIF for SnPb solderjoints. However, due to viscoplastic/creep deformation of solder al-loys that are captured by the Anand constant/model (values shownin Table 2 and the embedded Macro of Anand Model in ANSYS), thelocal stress/strain tends to relax with the further loading time.Therefore, the SIF values again decreases. Yet, the competition

580 M.O. Alam et al. / Computational Materials Science 45 (2009) 576–583

between these two opposite forces depends on the thickness of sol-der layer, crack locations etc.

This numerical finding suggests that fracture strength of solderbutt-joint shear samples might be around 10–12 MPa for this kindof sample size/geometry and the crack size. In fact, in our experi-mental work on the BGA solder joint shear test, we have foundfracture strength varies between 10 and 25 MPa depending onthe solder alloys, pad metallizations and aging conditions. Brittlefractures through the IMC layer were also always associated withlower value of the shear strength. While crack size and statisticsin those experimental samples had not been investigated, a corre-lation of interfacial reactions product with the spread of the shearstrength has been described in Ref. [18]. On the other hand, KI andKII values for a tensile butt-solder joint increase with the applied

Fig. 6. The extent of deformation (shown as vonMises strain distribution) at the solderloading rate of 0.8 MPa/s.

loading at a slower rate and show peaks at around 80 MPa [13].It is worth mentioning here that experimental values of fracturestrength of the tensile butt-solder joint were reported in the rangeof 70–90 MPa in Refs. [5–7] that is also nearly coinciding with thesimulation result. Yet, the shear strength value of solder joints isfound (both experimentally and numerically) to be much lowerthan the tensile strength value.

Experimental findings in Ref. [19–21] confirm that critical val-ues for the fracture toughness (KIC) of the Cu6Sn5 IMC lie between1.4 and 3 MPa-m0.5. Considering the whole solder layer of the sol-der butt joint replaced by the IMC in this numerical analysis, wehave found the maximum value of K is around 0.3 MPa-m0.5 foran applied stress of 12 MPa. Therefore, in a shear sample ofIMC-butt joints (where solder is replaced by IMC), a crack will

region near the crack tips under the applied stress of (a) 12 MPa and (b) 18 MPa at

-1

0

1

2

3

4

5

6

7

8

0 5 10 15 20

Applied Loading (Stress, MPa)

SIF

, MP

a-m

0.5

KI, 1 micron

KII, 1 micron

KI, 10 mircon

KII, 10 micron

K -critical

Fig. 8. Comparison of SIF values of solder butt-joint shear samples of Pb-freesolders between two crack positions from the IMC-solder interface with the appliedloading (solder layer thickness is 1mm, and loading rate is 0.8 MPa/s).

M.O. Alam et al. / Computational Materials Science 45 (2009) 576–583 581

not propagate at r = 12 MPa when the crack size, a = 10 lm. How-ever, in the present numerical analysis, KI/KII values of IMC exceedthe critical value of 1.4 MPa-m0.5 for the same loading stress, r andthe same crack size, a. Therefore, cracks would propagate under theapplied load of 12 MPa that is the fracture strength of solder joints.

Fig. 6 compares vonMises strain distribution at the solder re-gion near the crack tips at the applied stress of 12 MPa (a) and18 MPa (b). The extent of crack opening is higher at the appliedstress of 12 MPa (see Fig. 6a), where we have found higher SIF val-ues (see Fig. 5). With the continued application of stress, the solderregion exerts higher localized deformation, however, as the loadingrate is only 0.8 MPa/s, there is a sufficient time simultaneously forthe stress relaxation of solder alloy at very near to the interface.Therefore, crack tip opening is reduced (see Fig. 6b) and resultsin lower SIF values (see Fig. 5).

3.2. Effect of crack locations relative to the interface

To understand the influence of the solder alloy on the crack po-sition near to the interface and further away, the same size ofcracks were considered at a distance of 1 lm, 2 lm, 5 lm, and10 lm from the IMC-solder interface. An applied load of 12 MPaand a loading rate of 0.8 MPa/s were used for both SAC and SnPbsolders. Fig. 7 shows the variation of KI and KII values with thecrack location (i.e. the distance between the crack and the IMC-sol-der interface). It is clear from the figure that SIF values increasessharply while the crack location approaches near to the interface,in particular, the KII value, i.e. the SIF of shear mode increases toa very high value that could lead to a very unstable crack. Fig. 8also reveals how the variation of KI and KII values related to the ap-plied loading and the crack location. The sharp increase in KI and KII

values for the crack located within 1 lm distance from the IMC-solder interface is clearly visible. Loading beyond 12 MPa startsto contribute higher KII values for the crack located 1 lm distanceapart from the IMC-solder interface. Whereas, there is no signifi-cant increase of KII values noticed for the crack located 10 lm dis-tance apart from the IMC-solder interface. Moreover, neither KII

values nor KI values have exceeded the fracture toughness value(1.5 MPa-m0.5) of the solder joints, whereas these SIF values forthe crack located 1 lm distance apart from the IMC-solder inter-face exceeded 1.5 MPa-m0.5 after the shear loading of 10 MPa.

From Fig. 7, it is also revealed that Pb-free solder (SAC) contrib-utes higher values compared to the SnPb solder for the crack lo-cated 1 lm distance apart from the IMC-solder interface. This isbelieved to be slower stress relaxation (i.e., lower creep strain) ofPb-free solders under the localized stress/strain for the case ofthe crack located at 1 lm distance form the interface. It is seen that

SAC SnPb

KII

1

0

1

2

3

4

5

6

7

SIF,

MP

a-m

^0.

5

Distance from the

interface, m

10

5

2

1

KI KII KI10

52

Fig. 7. Effect of the crack position from the IMC-solder interface on the KI and KII

values of Pb-free and SnPb solder joint samples. (solder layer thickness is 1mm,applied load is 12 MPa and loading rate is 0.8 MPa/s).

cracks within 5 lm distance form the interface exerts more than1.5 MPa-m0.5 – higher value than the experimental KC values ofIMC that could lead to fracture near the interface. Among KI andKII values, KII values were found to be very sensitive to the cracklocation, in particular, for Pb-free solder that is again due to itshigher creep resistance. An effect of thickness of the IMC layerwas also studied where crack location was considered at the mid-dle of the IMC layer. IMC layers of 2 lm, 4 lm, 10 lm, and 20 lmhaving a crack at the middle of the IMC layer resulted nearly thesame SIF values as shown in Fig. 7 for crack distances of 1 lm,2 lm, 5 lm, and 10 lm, respectively. Therefore, we conclude thatthinner IMC layers have strong effect on the SIF – leading to unsta-ble cracks.

Fig. 9 shows vonMises stress distribution at the crack tips aswell as the extent of crack tip openings for the cracks within1 lm (a), 2 lm (b) and 5 lm (c) distances from the interface. Com-parative crack opening displacements are clearly visible dependingon the location of the crack from the interfaces. This simulation re-sult also agrees qualitatively with the results of other simulationworks carried out by Tilbrook et al. [22] who conducted effects ofplastic yielding on crack propagation near ductile/brittle interfacesof Cu/W. They used the term, ‘Anti-sheilding’ to express stressintensity factor amplifications due to the compliance mismatch be-tween the elastic/plastic properties of ductile (Cu) and brittle (W)materials. While Tilbrook et al. considered relatively larger sam-ples with high–strength materials combination, this present re-search deals with small-sized samples and rather soft solderalloys. Therefore, the effect of compliance mismatch due to elasticand viscoplasitc deformation of soft solder has been noticed withinonly few microns of distance from the IMC-solder interface.

Along with KI and KII values, the direction of crack path, h is alsoan important fracture mechanics parameter that is used to predictthe crack propagation direction. This is also known as ‘kink angle’.There are several methods to measure h. Among them, maximumcircumferential stress theory is used to compute h [13,23] for thepresent calculation.

Fig. 10 shows the variation of kink angle, h with the crack loca-tion for the present model. It is revealed from the curves that cracknear to the solder interface deviate to the solder region at a higherdegree than that of the crack far distance from the interface – obvi-ously kink angle increases with the applied load. However, afterreaching a peak, kink angle again decreases with the applied load-ing. Under a specific loading rate such as 0.8 MPa/s used for thisstudy, solder alloys have the opportunities for stress relaxationeven though the applied stress goes higher. This time dependentstress relaxation reduces stress field around the crack tip. In fact,

Fig. 9. vonMises stress distribution at the crack tips as well as crack openings for the cracks position of (a) 1 lm, (b) 2 lm and (c) 5 lm from the IMC-Pb-free solder interface(solder layer thickness is 1mm, temperature is 25 �C (298 K) and loading rate is 0.8 MPa/s).

582 M.O. Alam et al. / Computational Materials Science 45 (2009) 576–583

if fracture toughness reaches the critical value, the fracture propa-gates before we see any off-peak decrease in kink angle. For thecrack near the interface, the peak value of kink angle was foundat around 12 MPa – that is a typical value of fracture strength ofsolder joints found both from the current finite element analysisand the previous experimental work.

3.3. Effect of solder thicknesses

Without any solder alloys between the Cu plates, sandwichedby only elastic IMC, the KI value lies within �0.5 MPa-m0.5. Never-theless, the SIF value increases significantly with the presence ofsolder alloys – the thicker the solder layer, the higher the valuesof SIFs. Fig. 11 shows the variation of KI and KII values of Pb-freesolders with the solder layer thickness and applied load, at theloading rate of 0.8 MPa/s for the crack located at 1lm distanceapart from the IMC-solder interface. In general, higher SIF values

are noticed for thick solder joint samples. Higher values of SIF withthe increasing solder layer thickness are considered to be related tothe mass effect of solder alloys. The thicker solder layer exerts ahigher total viscoelastic deformation that results in a higher com-pliance mismatch between the neighbouring IMC layer and the sol-der layer and therefore, contributes a higher stress near the cracktip in the elastic IMC region.

4. Conclusion

A simplistic numerical study carried out in this research showsa reasonable agreement of fracture strength values of shear butt-solder joints with the experimental findings from our previousshear test results of BGA solder joints. Although the crack sizeand the crack distribution inside the IMC layer in a real solder joint(as well as the loading condition) might vary within a wide range,the simulation result proves that the crack nearer the interface is

-80

-70

-60

-50

-40

-30

-20

-10

0

100 5 10 15 20

Applied Loading, MPa

Kin

k A

ngle

,

crack at 1 microndepth-SnAg

crack at 1 microndepth-SnPb

crack at 2 microndepth-SnAg

crack at 2 microndepth-SnPb

crack at 5 microndepth-SnAgcrack at 5 microndepth-SnPb

crack at 10 microndepth-SnAg

crack at 10 microndepth-SnPb

θ

Fig. 10. Relationship of crack deflection angle, h, with the applied stress and crackpositions from the IMC-Pb-free solder interface. (Solder layer thickness is 1mm andloading rate is 0.8 MPa/s).

0

1

2

3

4

5

6

7

8

0 5 10 15 20

Applied Loading (Stress, MPa)

SIF

, MP

a-m

^0.

5

KI, 0.3 mm

KII, 0.3 mm

KI 0.5 mm

KII, 0.5 mm

KI , 1 mm

KII, 1 mm

Fig. 11. Effect of solder layer thickness on the KI and KII values of Pb-free solders.(The crack position from the IMC-solder interface is 1lm, and loading rate is0.8 MPa/s).

M.O. Alam et al. / Computational Materials Science 45 (2009) 576–583 583

always more prone to propagate. The crack nearer the interfacealso deflects toward the solder side easily. The thicker solder layerhas also found to have a detrimental effect on the fracture charac-teristics of the solder joints. For the crack positions near to theIMC-solder interface, higher values of KI and KII values are foundin the solder joint of SnAgCu, than that of the SnPb solder. How-ever, with the crack position further away from the IMC-solder,there is no significant difference noticed between Pb-free and SnPb

solder joints. It has been concluded that soft solder matrix gener-ates a non-uniform and transient elastic-plastic deformation acrossthe IMC-solder interface that changes stress states at the IMC layernear the solder region which increases KI and KII values and there-fore, reduces fracture toughness of solder joints.

Acknowledgement

The authors would like to acknowledge the EU funded MarieCurie Incoming International Fellowship, individual driven projectMIFICT-2006-022113, ‘‘Reliability study of fine-pitch area-arrayPb-free solder joints for advanced electronic packaging – effect ofintermetallic compounds”.

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