ACTA MECHANICA SINICA (English Series), Vol.18, No.3, June 2002 The Chinese Society of Theoretical and Applied Mechanics Chinese Journal of Mechanics Press, Beijing, China Allerton Press, INC., New York, U.S.A.

ISSN 0567-7718

QUICK ASSESSMENT METHODOLOGY FOR RELIABILITY OF S O L D E R J O I N T S IN BALL G R I D A R R A Y ( B G A ) ASSEMBLY P A R T I: C R E E P C O N S T I T U T I V E R E L A T I O N A N D F A T I G U E MODEL* Shi Xunqing (~iJll~) 1 Wang Zhiping ( : ~ z ) 2 John HL Pang 2 Zhang Xueren ( ~ ) 1 Nie Jingxu ( ~ ) 1 l(Dept, of Power Eng., Beijing Univ. of Aeronautics & Astronautics, Beijing 100083, China)

2(School of Mech. ~ Prod. Eng., Nanyang Technological Univ., Nanyang Avenue, Singapore 639798) In this study, a new unified creep constitutive relation axld a modified energy-based fatigue model have been established respectively to describe the creep flow and predict the fatigue life of Sn-Pb solders. It is found that the relation successfully elucidates the creep mechanism related to current constitutive relations. The model can be used to describe the temperature and frequency dependent low cycle fatigue behavior of the solder. The relation and the model axe further employed in part II to develop the numerical simulation approach for the long-term reliability assessment of the plastic ball grid array (BGA) assembly. ABSTRACT:

K E Y W O R D S : dislocation controlled creep flow, creep-fatigue interaction, constitutive relation, life prediction model, solder joint reliability

1 INTRODUCTION The requirements of high density i n h i g h - s p e e d circuitry are driving the design of surface mount components (SMC) to ever increasing I / O counts and smaller package size. Ball grid array (BGA) technology has been making good progress with the evolution from peripheral to area-array packaging technology. Surface mount solder attachment plays an important role in BGA packages since the solder joints not only provide the electrical interconnection but are also the sole mechanical attachment of the electronic components to the printed circuit board (PCB). However, the stresses caused by the temperature gradients and the cyclic temperature fluctuations constitute a condition of viscous creep flow for a constrained solder joint [1]. At the same time, the constrained solder joints are cycled between the maximum and minimum temperature limits depending on the environment. This is due to the mismatch of the coefficient of thermal expansion (CTE) between the components in the package. Those creep and creep-fatigue interactions result in most of failures in solder joints. Therefore, surface mount solder attachment requires the special reliability assessment to assure long-term reliability of a P C B assemblies. Received 4 December 2000, revised 11 May 2001 * The project supported by the National Natural Science Foundation of China (59705008)

Vol.18, No.3 Shi XQ et al.: Assessment Method of Solder Joints in BGA Assembly--Part I 275 Accelerated thermal cycling (ATC) tests are widely employed to validate the reliability of solder joints. But it normally takes several months to complete a test and is very expensive and time-consuming. Hence, highly accelerated reliability testing method that reduces the cycle time is greatly sought for. In this study, a new mechanical deflection system (MDS) was established for quick reliability assessment of the solder joints in BGA assembly. To numerically not only experimentally establish the methodology, the creep constitutive relation and the fatigue life model must be firstly established. Simple Arrhenius power-law creep constitutive relations[ 2,3] have been widely employed to predict the high temperature creep flow of Sn-Pb solders during past fifteen years. However, those relations were found to break down at high stresses and are incapable of explaining the issues that the values of stress exponent and activation energy are temperature dependent[ a]. As a consequence, Darveaux developed the hyperbolic-sine formulae for SnPb solders [5]. The formulae can describe the creep flow for low stress and also for high stress at which the simple power-law breaks down, but it failed to explain the temperature dependencies of stress exponent and activation energy. On the other hand, a two-regime power-law constitutive relation has been proposed in recent research works [6,7]. However, the relation causes a confusion of creep deformation mechanism. More seriously, the values of stress exponent and activation energy in the relation were found to differ considerably in different Refs.[5~8]. The above issues strongly suggest that some important physical quantity is missing from the existing relations. Strain-based models have been extensively used to characterize the low cycle fatigue behavior of solder alloys [9'1~ However, the models were found to be incapable of describing the temperature and frequency dependencies of the low cycle fatigue behavior[ n] . In addition, it is practically very difficult to obtain a single inelastic strain value in a solder joint because of the complex stress-state [12]. In contrast, it is much easier to calculate strain energy density from the stress-strain hysteresis loops for any types of solder joints [13]. Therefore, in recent years, energy-based models have been increasingly used to predict the fatigue life of solder alloys in terms of the strain energy density [14]. These models are not so well established as the strain-based ones, and some researchers [15] even expressed doubt on whether the strain energy density is a true parameter governing fatigue life of solder alloys. In part I, a great number of creep and fatigue tests have been carried out to investigate the high temperature creep and low cycle fatigue behavior of a 63Sn/37Pb solder alloy. Subsequently, the results were used to solve the issues related to the existing creep constitutive relations and low cycle fatigue models. As a result, a new unified creep constitutive relation and a modified energy-based fatigue model were proposed. In part II, the relation and model were used to construct a basis of MDS numerical approach for quick reliability assessment of solder interconnections. 2 EXPERIMENTAL

METHODS

The material used in the study was a eutectic alloy 63Sn/37Pb. This material is widely used as solder interconnection in BGA assembly. Both rectangular creep specimens and round fatigue specimens were prepared by machining the solder bars of high purity as-cast 63Sn/37Pb. The geometry and dimensions of the samples are shown in Fig.l, After machining, the gauge section of each specimen was carefully ground on fine SiC paper and polished using 1 # m diamond paste. Afterwards, the specimens were annealed at 60~ for

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0.5

(a) Creep specimen r = 12

r =. 6

p=

to5

50 90 (b) Fatigue specimen Fig.1 Geometry and dimensions (Unit: ram) 24 h in a n N2 a t m o s p h e r e to e l i m i n a t e t h e r e s i d u a l stresses. T h e creep t e s t s were c o n d u c t e d on a micro-force t e s t s y s t e m f r o m M T S . T h e s y s t e m has t h e c a p a b i l i t y t o h o l d t h e c o n s t a n t l o a d w i t h o u t d r o p . A special d e s i g n e d e n v i r o n m e n t a l c h a m b e r r a t e d from - 6 5 ~ t o 250~ was m o u n t e d o n t o t h e s y s t e m for r u n n i n g t h e creep t e s t s a t low a n d high t e m p e r a t u r e s . I n t h e tests, s p e c i m e n s were d e f o r m e d in t e n s i o n w i t h a c o n s t a n t stress control. A n e x t e n s o m e t e r was e m p l o y e d to m e a s u r e t h e s t r a i n of t h e specimens. T h e t e s t p r o g r a m is given in T a b l e 1. T h r e e s a m p l e s were t e s t e d p e r t e s t c o n d i t i o n a n d t h e r e s u l t s were a v e r a g e d t o reduce t h e e x p e r i m e n t a l error. T a b l e 1 C r e e p t e s t p r o g r a m o f 6 3 S n / 3 7 " P b solder Stress/MPa --40 1.25 2 3.25 5 10 15 20 25 30 40 50 70

3 3 3 3 3 3

25 3 3 3 3 3 3 3 3 3

Temperature/( ~C) 75 125 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3

3

150 3 3 3 3 3 3 3 3

T h e fatigue t e s t s were c o n d u c t e d on a n M T S s e r v o - h y d r a u l i c t e s t i n g m a c h i n e ( m o d e l 810). T h e t e s t s were r u n u n d e r a s y m m e t r i c a l u n i a x i a l t e n s i o n - c o m p r e s s i o n l o a d i n g w i t h t o t a l s t r a i n control. D u r i n g t h e t e s t i n g , t h e c r o s s h e a d was r e v e r s e d w h e n e v e r h a l f of t h e r e q u i r e d t o t a l s t r a i n was a t t a i n e d . T h e s t r a i n was m o n i t o r e d using a n e x t e n s o m e t e r a t t a c h e d

Vol.18, No.3 Shi XQ et al.: Assessment Method of Solder Joints in BGA Assembly--Part I 277 to the gauge length of the fatigue specimen. The details of the test program are given in Table 2. For each test condition, six specimens were tested and the average value of the six readings was taken as the fatigue life. Table 2 T e m p e r a t u r e / ( ~ C)

Fatigue

test

program

Frequency/Hz

Total strain/% 0.5

--40

1

2

5

6

6

6

6

6

6

6

6

6

6

6

10- 2

6

6

6

6

6

6

6

6

6

6

6

6

6

6

6

6

6

6

6

6

10 - 1

6

6

6

6

6

6

10 - 2

6

6

6

6

6

6

10 - 3

6

6

6

6

6

6

10 - 4

6

6

6

6

6

6

6

6

6

6

6

6

1

6

6

10- I

6

6

6

6

6

6

10- 2

6

6

6

6

6

6

10- 3

6

6

6

6

10- 4

6

6

6

6

1

6

6

6

6

6

6

6

6

6

6

6

6

6

10- 2

6

6

6

6

10- 3

6

6

6

6

10- 4

6

6

6

6

10- I

1

6

6

6

6

6

6

6

6

6

6

6

6

10- 2

6

6

6

6

10- 3

6

6

6

6

10- 4

6

6

6

6

10- I

150

3 HIGH TEMPERATURE

50

6

1

125

25

1

10- 4

75

10

10- I

10- 3

25

solder

of 63Sn/37Pb

6

C R E E P B E H A V I O R OF 6 3 S n / 3 7 P b S O L D E R

3.1 E x p e r i m e n t a l R e s u l t s and D i s c u s s i o n For all the creep tests, the creep-time curves display three stages, namely primary, secondary and tertiary creep. Attention of the study was focused on steady-state (secondary) creep since it dominates the creep rupture life of the solder Ira] . The tensile stress and strain were converted into shear stress and strain using yon Mises yield criterion [16]. The test results are presented in Fig.2. The simple Arrhenius power-law constitutive relation [171 was used to describe the steady-state creep strain rate d % r / d t of Sn-Pb solders in terms of the applied shear stress T, as shown below

d~fcr/dt~-dTnexp( - Q )

(1)

where n is the stress exponent, Q is the activation energy, T is the absolute temperature, R is Boltzmann's constant, and A is a constant.

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With the assumption that the creep deformation mechanism does not change at the temperature range of - 4 0 ~ to 150~ some researchers [2,3,5] suggest that the activation energy is kept constant for the whole temperature range studied. Under logarithmic coordinates, Eq.(1) gives a linear relationship between the creep strain rate and applied stress. The slope of the linear curve represents the stress exponent n. However, it is noted from Fig.2 that all curves show nonlinear characteristic for the whole stress range. In other words, the curve displays a good linearity only at the low stress regime. It indicates that the Arrhenius relation is only applicable for the low stress regime and breaks down at the high stress regime. When the relation was applied for the low stress regime, the n values were then determined as plotted in Fig.3. It is observed that the n value decreases with increasing temperature. Therefore, the issue caused is that the relation is incapable of explaining the experimental fact that the stress exponent is temperature dependent. l0 s

101 100

\ lO-1 lO

temperature - , - -40~ -.-

,5~176

+

75~

6

# A#*

/J

....................

~'5

iii

v

rI v

04

"i~ ' ,10 510-s10-910 10-3 ~41010_, 2,'"_--i's"'"~"' '"125~ ,' ' "-'" '""'""' / d / ~' '" //" ....................

•

3

10_10 ,i,.,...,,,,, . ..,.~.,...,...,...,,,,, . ..,...,...,...,...,,,, s 4~s 100 2 3 45s 101 2 3 45s 102

i

l

--50

i

l

i

l

i

l

i

--I0

l

i

l

30

l

,

i

,

70

i

,

i

II0

150

T/(~

shear stress/MPa Fig.2 Steady-state creep behavior at different temperatures For a given stable microstructure and applied stress, under logarithmic coordinates, Eq.(1) gives a linear relationship between the creep strain rate and the reciprocal of absolute temperature. The slope of the linear curve represents the activation energy Q. Unfortunately, as can b e seen in Fig.4, the experimental results display nonlinear characteristic for any given stress level. If the activation energy was determined from different points of the curve, the Q value "must" be different. Hence, it is not surprising why there are so large differences in the Q value, ranging from 3 2 . 5 k J / m o l to 86.5 kJ/mol, used in different models [5~s].

i

Fig.3 Stress exponent n as a function of temperature for the low stress regime

7

~

OJ

b

101 10~ 10-1 10-2 10-3 10-4 10-5 10-6 10-7 lO-S 10-9 10-1o

o~

'

'

0.002

'

--~

23 09'MPa

shear stress - . o - 1 7 1 3 2 M P a

%% ~x ~x "~ "~ ~ "~ ~ ~

--4- 11.55MPa --o- 5.77Mea ~ 2.89MPa -'r 1.88MPa -*- 1.16MPa

i

i

0.003

0.004

0.005

reciprocalof temperature/K-1

Fig.4 Steady-state creep strain rate versus reciprocal of absolute temperature

Vo1.18, No.3 Shi XQ et al.: Assessment Method of Solder Joints in BGA Assembly--Part I 279 To solve the above issues, a hyperbolic-sine power-law relation is currently employed to describe the high temperature creep behavior of Sn-Pb solders [5], given by d%~/dt = A ~G [sink ( a G ) ] n exp ( - R ~ )

(2)

where G is the shear modulus, which is used to normalize the shear stress; a is a temperatureindependent parameter, which is related to the stress level where the power-law breaks down. It was found that the hyperbolic-sine relation is capable of describing the creep behavior of Sn-Pb solders over a wide range of stress. However, it still cannot be used to explain the temperature dependency of stress exponent. Another attempt, which is repeatedly tried to describe the creep behavior of Sn-Pb solders, is the two-regime power-law relation, as shown below [6~s]

d%r/dt=A1G

exp

--~-~

+A2~ ~)

exp

Q2

where A1 and A2 are material constants, nl and n2 are the stress exponents, Q1 and Q2 are the activation energies, and the subscripts 1 and 2 represent the low temperature grain boundary creep and high temperature matrix creep at low stress regime, respectively. This relation is shown to be applicable for the whole stress regime and most of temperature range (-40~ to 150~ However, the relation brings out a confusion that the stress exponent and activation energy used in the second "term" of Eq.(3) are for different creep processes, which is not in agreement with the Arrhenious power-law rate-controlling creep mechanism.

3.2 Unified Creep Constitutive Relation for 6 3 8 n / 3 7 P b Solder It is noted from Fig.4 that the curves exhibit good linearity in a small temperature range. In other words, it is reasonable to assume that the small change in temperature does not change the alloy microstructure and the creep rate-controlling mechanism. As a consequence, a new measurement method, so-called temperature differential creep test method, was proposed to determine the activation energy in this study. Under a given stress at the initial temperature 7'1, the temperature is changed abruptly to 7'2, which is slightly above T1. The difference in the steady-state creep strain rate associated with 7"1 and T2 is recorded. The activation energy Q for the creep process can be calculated by Q=

R In [(d%rl/dt)/(d%r2/dt)] (1/T2 - 1/T1)

(4)

where d % r l / d t and d%r2/dt are the creep strain rates at the temperatures 7"1 and T2, respectively. Using this method, a large number of creep tests were carried out at certain shear stress level and temperature. Subsequently, Eq.(4) was used to calculate the Q values at any tested shear stress and temperature. In the analysis, the shear stress was normalized by the shear modulus G, given by [1] G -- (24 782 - 39.63T) MPa

(5)

TypicM results are presented in Fig.5. It can be seen that the activation energy increases with increasing temperature, but it shows a nonlinear trend. The Q value at the high temperature regime (125~ to 150~ is much bigger than that at the low temperature regime (-40~ to 25~ and changes drastically at the intermediate temperature regime

280

ACTA MECHANICA SINICA (English Series) 90

,

.

,

i

,

J

2002

(25~ to 125~ Since the activation energy represents the energy barrier to be over80 come so that an atom might move from higher energy location to lower energy loca"-" 70 tion, the above experimental observation indicates that there should be a creep mecha~ 60 nism transition when the temperature is increased from low regime to high regime. 5o For 63Sn/37Pb solder alloy, - 4 0 ~ is 0.51 times of the melting temperature of the 40 alloy. It is well-known that when the am-50 0 50 100 150 200 bient temperature is above 0.4 times of the T/(~ melting temperature of alloys, the dislocaFig.5 Activation energy as a function of tion is thermally activated to glide along temperature at a given normalized the slip plane by cutting or by-passing a shear stress level of "r/G = 3.5 x set of obstacles. This rate-controlling pro10-4 cess is the diffusive motion of single ions or vacancies to or from the activated glide of the dislocation itself. This creep flow is usually referred as to core-diffusion control creep. In comparison, 125~ is 0.87 times of the melting temperature of the aUoy. At this very high temperature, dislocations acquire a new degree of freedom: they can climb as well as glide. The average velocity of dislocation is'determined mainly by the climb step. This high temperature climb creep is generally lattice-diffusion controlled[IS]. With the assumption that both dislocation core-diffusion and lattice-diffusion contribute significantly to the overall diffusive transport of matter, and one of them becomes the dominant transport mechanism under certain circumstances, an effective diffusion coefficient Deft was then defined to include those two mechanisms o-U

~

i

i

i

(6)

D e f = D i l l + Dcf~

where fr and ~ are the fractions of atom sites, and Dr and/91 axe the diffusion coefficients, as given by De --- Doc exp

-

D1 = Do1 exp

(Q1) - ~-~

(7)

where Doc and Dol axe the pre-exponential material constants, Qc and Q1 axe the activation energies, and the subscripts c and 1 represent the core-diffusion and lattice-diffusion, respectively. The value of ~ is essentially unity. The value of fr is determined by the dislocation density, p A = aop (S) where ac is the cross-sectional area of the dislocation core in which fast diffusion is taking place. At steady-state, p is a function of stress and temperature only. The simplest function, and the one consistent with both theory and experiment, isDS] p ~ B'

(9)

where B' is a material constant. By substituting Eqs.(8) and (9) into Eq.(6), the effective diffusion coefficient can be obtained, by

V o l . 1 8 , N o . 3 Shi X Q et al.: A s s e s s m e n t M e t h o d

o f S o l d e r J o i n t s in B G A A s s e m b l y ~ P a r t

Deft=D1 [ I + B ( G ) 2 D=]

I 281

(10)

where B is a constant. By replacing the diffusion coefficient in Eq.(2) with the effective diffusion coefficient given in Eq.(lO), a new unified creep constitutive relation was established G [sinh(~5)] d~//dt = A=~

nr exp ( R- ~ )

-4- A l ~ [sinh(oLG)]

TM

1)(11) exp ( Q--~--~

where Ac and At are constants, nc and nl are the stress exponents. The constants and parameters were determined by the same method used in Ref.[5] and are given in Table 3. Table 3 Material constants and parameters for b o t h low and high t e m p e r a t u r e creeps Material constant low temperature core-diffusion controlled creep high temperature lattice-diffusion controlled creep

Power-law breakdown parameter

Stress exponent

Activation energy /(kJ.mo1-1)

nc = 5

Qc=48.5

nl = 3

Q1 : 81.5

Ac = 2 X 10 -5 a = 1 289 AI : 2.5 X i0 -z

As can be seen in Fig.6, the new constitutive relation was found to describe very well the creep deformation of 63Sn/37Pb solder for different temperatures in a wide stress range. Most importantly, although the relation takes the same form as the two-regime power-law formulae given in Eq.(3), there is no confusion in the creep mechanism. The first term is for low temperature core-diffusion controlled power-law creep, while the second term is for high temperature lattice-diffusion controlled power-law creep. One of them becomes the dominant mechanism at the low or high temperature, since one term is much larger

101

.......................................................

.

.

.

.

#

,'

J lines for prediction of new relation ~. z s

temperature

io-~

~

i

;

r ,'

,--""*/", , ,"

25~

-

75 C ...",* , ~ ~, 125oC ....I~,," , ~ J 7 150oc ....,Zt. r II L ....~,,*" / ' - ,w ,,

10-4

~

.~

10_ 5

-,-

~,

10-7

..... . . . ""

,V;'~ ..,;:,'~

-4o~

4-

.m.-

9 ..

,,'~" *

7

,.. L""

| ,.

i0-9

i0-Io

,"

,.~'

symbols for experimental results

10-1

10 -s

>~ ...........

9

100

,.., ,., ,,'C

,, ,

s SO

9'

.

, ..~L'., ......., , , , ,

4 5s;

i0-4

2

,

3 4 56;i0-a

normalized shear stress

,

{.,.,.,.,.. 2

3 4

('r/G)

Fig.6 Comparison of creep strain rates obtained from the experiment and the new constitutive relation

282

ACTA MECHANICA

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2002

than another one at certain condition. It was also found that the relation can be employed to determine the values of n and Q for any given temperature, the results are in good agreement with the experimental data. It is therefore concluded that Eq.(ll) provides a good explanation of the temperature dependencies of stress exponent and activation energy. 4 LOW CYCLE FATIGUE BEHAVIOR OF 638n/37Pb SOLDER 4.1 E x p e r i m e n t a l R e s u l t s a n d D i s c u s s i o n

It was observed from the fatigue tests that the fatigue life tends to linearly decrease with increasing total strain or testing temperature for a certain testing frequency. However, the relationship between the fatigue life and frequency exhibits bi-linear characteristics, as shown in Fig.7. When the frequency is above 10 -3 Hz, the fatigue life is weakly dependent on the frequency. While when the frequency is below 10 -3 Hz, the fatigue life decreases drastically. 2

.,,,~

Jr~*ttlr,,,t

it~Nttt','t

~ftllrl','l

itttHtl','t

~tlllt.','t

IrttH

10 3

2

~'10 2 8

~

a

--~ 2 ,~u 101 ,,,., /" 3

2

X 0 9 [] 9 A 9

temp=25~ C, strain=2% temp=25~ strain=5% temp=25~ kemp=75~C, straln=5% temp--75~ strain----lO% temp=125~ C, strain=5% temp=125 ~ C, strain=lO%

........................ 10;0 _~"~ .......................... 10-42 10"% '10-% 10-12 '"" 10~......... 2 101 ~,/Hz

Fig.7 Relationship between fatigue life and frequency at different temperatures and total strain ranges Recently, the energy-based Morrow model [13~151 has been increasingly used to describe the low cycle fatigue life Nf of Sn-Pb solders in terms of the plastic strain energy density Wp, given b y N~nWp = C (12) where m is the fatigue exponent, and C is the material ductility coefficient. The plastic strain energy density was determined from the area within the stable stress-strain hysteresis loop. As shown by the solid line in Fig.8, the fatigue life obtained at a fixed test temperature (25~ and frequency (1 Hz) but at different total strain levels (0.5% to 50%) displays a linear relationship with the strain energy density. It means that the Morrow model predicts well a linear relationship between log Nf and log Wp. However, two issues were noted. Firstly, the model, in which the constants are determined at a certain frequency (e.g., 1 Hz), are not suitable for other frequencies (e.g., 10 -1 to 10 -4 Hz). The prediction leaves a very

Vol.18, No.3 Shi XQ et al.: Assessment Method of Solder Joints in BGA Assembly--Part I 283

large scatter band for any given total strain range, as presented by the dotted line in Fig.8. Similarly, the model, in which the constants are determined at certain temperature (e.g., 25~ is not applicable for other temperatures (e.g., -40~ 75~ 125~ and 150~ Again, there is a large scatter band for any given total strain range, as shown by the dotted line in Fig.9. 10 2

10~

~""

~

v=l H~,

4'~ A

i0 ~ 2

lO-t

~

10 ~

:oooo1.

10--3

,

,,,r. ,..,.,., ....... .,.,-., .....

T--40~

I0~

\

9, o . ~ s , t o t a l

10-~ : : . - o ~ . s , !-~-- ~'

~x~.

, , , . ,

~ T

Wpvariations, w:l Hz

2

,. r..., ....... . . , - . .......

.,-o- T 3 "~'" T 2 I.,.,

variations, total strain=lO%

:................. . . , , , , .

_

_\

10-I

stmin=2%~

total stcain=S% "~

variations, total strain----g% 9 variations,total strain----lO%

10-2

, . ..................... k~................

1002 1012 1022 1032 I042

sQ~

I0o2 3 10123 10223

1052 106

N~ (cyclesto failure)

Nf

10323

10423

105

(cyclesto failure)

Fig.9 Typical curves of strain energy density versus fatigue life show the temperature variations at 1 Hz

Fig.8 Typical curves of strain energy density versus fatigue life show the frequency variations at 25~

A frequency-modified Solomon model, which incorporates both the frequency-modified strain energy density W p / v n and the frequency-modified fatigue life Nfv (k-l), was proposed to solve the above issues[ 15] =

L

J

/2 n

where v is the frequency, k and n are the frequency exponents. Unfortunately, the C value in this model is still strongly dependent on temperature, and it decreases from 250 to 5 as the temperature increases from - 5 0 ~ to 150~ [15]. Therefore, Solomon et al. expressed doubt on whether the energy density is a true parameter governing fatigue life of solder alloy. 4.2 M o d i f i e d E n e r g y - B a s e d F a t i g u e M o d e l for 6 3 S n / 3 7 P b S o l d e r As mentioned in Section 3.2, when the operating temperature is above 0.4 times of the melting point of alloys, the dislocations are thermally activated to glide along the slip plane as well as climb to the next adjacent slip plane. It is recognized that the stress is required to move the dislocations. From the point of view of energy, those stress driven glide and climb processes lead to the energy dissipation. When the dissipated energy is cumulated to the critical level, the failure occurs in the material. It was observed from the experiment that the plastic strain energy density, which is related to the dissipated energy, is frequency and temperature dependent. Typical experimental results are presented in Figs.10 and 11 to illustrate the effects of frequency and temperature on the plastic strain energy density. At certain total strain range and test temperature, the area within the hysteresis loop decreases with decreasing frequency (Fig.10). While at certain total strain and frequency, the area of hysteresis loop decreases with increasing temperature (Fig.ll). Therefore, it is necessary for fatigue life prediction of the

ACTA MECHANICA SINICA (English Series)

284

5O stress/MPa

2002

50

stress/MPa

30 10 i

--5,

i

.

i

-4 -3 -2 -110

,

.

,

9

,

.

,

,,

,

1 2 3 4J5

- 5 - 4 - 3 - 2 -11 L - - ..............

.....

strain/%

-30

-3O

-50 (b) 10 -4Hz

(a) 1Hz

Fig.10 Hysteresis loops obtained at two typical frequencies at 25~ stress/MPa

5O

10 i

i

r

-4 --3 --2 -_110

1

2

3

4

......

strain/%

-3O

(a) 25~

(b) 150~

Fig.ll Hysteresis loops obtained at two typical temperatures levels at 1 Hz solder to modify the plastic strain energy by taking into consideration of those temperature and frequency dependencies. The energy-based Morrow model ignores the frequency dependency, so it is not surprising that it can not describe the creep-fatigue interaction at different frequencies. The Solomon frequency-modified energy-based model takes the frequency dependency into proper account, but does not account for the temperature influence, so the "constant" C in the model is not independent of temperature. The analysis indicates that a temperaturedependent material parameter must be introduced into the frequency-modified energy model so that both frequency and temperature dependencies of plastic strain energy density can be considered. From Fig.ll, it can be seen that when the test temperature increases, the plastic strain energy density decreases, but the plastic strain is roughly kept as a constant. It means that the true parameter, which leads to the reduction in the area of hysteresis loop, is the flow stress [14]. Therefore, by introducing the flow stress at into the frequency-modified energy-

Vol.18, No.3 Shi XQ et al.: Assessment Method of Solder Joints in BGA Assembly--Part 1 285 based model, a new model was proposed, as shown below

~~/N~,(~_~)/~ Wp= /

j

c

2crf

(14)

Based on the theory of plastic flow, the frequency exponent k was found to be independent of strain range[ 11] and determined by the same method used in Ref.[15]. The k values at the two frequency ranges were used to calculate the frequency modified coefficient v (k-l), i.e. V(k-l) =

(i% V

(ks-1 )

(10 -3)

(kl--1)

(15)

10 -3 Hz > v _> 10 -4 Hz

for

As can be seen in Fig.12, when the frequency modified fatigue life Nfv(k-l) was plotted as a function of the flow stress modified energy density Wp/2crf, all data obtained at a wide range of frequency (i to 10-4 Hz) fall into roughly the same point for any given total strain level. It means that there is no more frequency variation, in other words, the values of m and C are constants. Similarly, the constants of m and C can be determined for other temperatures. The results are presented in Fig.13. It is noted that the constants are relatively temperature-independent. Therefore, the average values of m and C over the temperature range can be used to make a reasonable fit to all the experimental data. Finally, the constants in the model were found to be: m -- 0.69, C -- 1.70, kl = 0.9, and k2 --- 0.4.

101

-,

,,,,,.,

,,,,,.,

-,

,,,

......

,

,

,,,,,,,-.

,

,F,,,,,.,

,

,,,,

3

,

,

.

.

.

.

.

,

.

.

.

.

.

.

.

,

,

3

-4- fatigue exponent (m) 4 - ductility coefficient ((7)

v: 1 Hz,'-,0.0001 Hz

2

10o

-,

9

2

2

10 -1

lo A 2

10-3 A

A

=.

2

10-4

-~--

v variations, total strain=lO%

2

I 0 - 1 0 ~ i ,,.,,,.,.,1012, ,.,,.,,,t10 22 ,,..,, , 1 032 1llqlll .,.110 42 ,,,,,,..~1052,,,,.106

Nfv (k-l) (cycles to failure) Fig.12 TypicM curves of flow stressmodified strain energy density versus frequency-modified fatigue life at 25~

0

-50

'

i

.

i

--10

,

i

,

,

30

.

i

,

,

70

.

,

.

,

.

110

I

.

,

0

150

T/(~ Fig.13 Constants in the stress modified energy-based fatigue model as functions of temperature

5 CONCLUSIONS When the simple Arrhenius power-law creep constitutive relation is used to describe the high t e m p e r a t u r e creep behavior of the solder, it was found to be inapplicable to the cases for high stresses over the t e m p e r a t u r e range of - 4 0 ~ to 150~ At low stresses, the stress exponent and the activation energy in the relation are found to be t e m p e r a t u r e dependent. Based on the assumption that b o t h dislocation core-diffusion and lattice-diffusion contribute significantly to the overall diffusive transport of matter, and one of t h e m becomes

286

ACTA MECHANICA SINICA (English Series)

2002

the dominant transport mechanism under certain circumstances, a new unified creep constitutive relation was established. It is found that the relation can be used not only to describe the creep flow of 63Sn/37Pb solder over the temperature range of - 4 0 ~ to 150~ but also to solve the issues of temperature dependency of exponent stress and activation energy. It is interesting to note that the variation in stress exponent with changing temperature is due to the assumption of activation energy being a constant. However, the temperature dependent activation energy is caused by the transition of creep deformation mechanism from the glide-controlled process to climb-controlled process. The energy-based Morrow model can not be used to describe the creep-fatigue interaction behavior of 63Sn/37Pb solder alloy, since it ignores the effect of frequency on fatigue life. The frequency-modified Solomon model takes into proper account the effect of frequency on fatigue life but does not account for the temperature influence, so the "constants" in the model are dependent on temperature. Flow behavior of 63Sn/37Pb solder was observed to be visco-plastic and strongly dependent on temperature; therefore, flow stress is introduced into the frequency-modified energy model to consider influence of temperature on the fatigue life. As a result, a new flow stress modified energy-based life prediction model is obtained and found to adequately describe the creep-fatigue interaction behavior at different temperatures. The above results may provide a theoretical basis to quickly assess the long-term reliability of solder interconnection with the numerical method. In part II, the creep constitutive relation will be used to work out the cumulative creep strain of the solder joints. Subsequently, the modified fatigue model will be employed to predict the fatigue life of the solder joints. REFERENCES 1 Shi XQ, Zhou W, Pang HLJ, et al. Effect of temperature and strain rate on mechanical properties of 63Sn/37Pb solder. ASME J of Electronic Packaging, 1999, 121(3): 179~186 2 Kashyap BP, Murty GS. Experimental constitutive relations for high temperature deformation of a Pb/Sn eutectic alloy. Materials Science and Engineering, 1981, 50:205~213 3 Pao YH, Badgley S, Jih E, et al. Constitutive behavior and low cycle thermal fatigue of 97Sn3Cu solder joints. ASME J of Electronic Packaging, 1993, 115(2): 147~152 4 Lau JH. Solder Joint Reliability Theory and Applications. New York: Van Nostrand Reinhold, 1991 5 Darveaux R, Banerji K. Constitutive relations for tin-based solder joints. IEEE Transactions on Components, Hybrids, and Manufacturing Technology, 1992, CHMT-15(6): 1013~1024 6 Knecht S, Fox LR. Constitutive relation and creep-fatigue life model for eutectic tin-lead solder. IEEE Transactions on Components, Hybrids, and Manufacturing Technology, 1990, CHMT13(2): 424~433 7 Hacke P, Sprecher AF, Conrad H. Computer simulation of thermo-mechanical fatigue of solder joints including microstructure coarsening. A S M E J of Electronic Packaging, 1993, 115(2): 153N158 8 Syed AR. Creep crack growth prediction of solder joints during temperature cycling an engineering approach. ASME J of Electronic Packaging, 1995, 117(2): 116~122 9 Solomon HD. Fatigue of 60/40 solder. IEEE Transactions on Components, Hybrids, and Manufacturing Technology, 1986, CHMT-9(4): 423~432 10 Guo Q, Cutiongco EC, Keer LM, et al. Thermomechanical fatigue life prediction of 63Sn/37Pb

Vol.18, No.3 Shi XQ et al.: Assessment Method of Solder Joints in BGA Assembly--Part I 287 solder. ASME J of Electronic Packaging, 1992, 114(2): 145~151 11 Shi XQ, Pang HLJ, Zhou W, et al. Low cycle fatigue analysis of temperature and frequency effect in eutectic solder alloy. International J of Fatigue, 2000. 217~228 12 Hong BZ, Yuan TD, Burrell L. Anisothermal fatigue analysis of solder joints in a convective CBGA package under power cycling. Sensing, Modeling and Simulation in Emerging Electronic Packaging , 1996, EEP-17(1): 39~46 13 Dasgupta A, Oyan C, Barker D, et al. Solder creep-fatigue analysis by an energy-partitioning approach. ASME J of Electronic Packaging, 1992, 114(2): 152~160 14 Shi XQ, Pang HLJ, Zhou W, et al. A modified energy-based low cycle fatigue model for eutectic solder alloy. Scripta Materialia, 1999, 41(3): 289~296 15 Solomon HD, Tolksdorf ED. Energy approach to the fatigue of 60/40 solder: part I influence of temperature and cycle frequency. ASME J of Electronic Packaging, 1995, 117(2): 130~135 16 Meyers MA, Chawla KK. Mechanical Metallurgy. New Jersey: Prentice-Hall, 1984 17 Hertzberg RW. Deformation and Fracture Mechanics of Engineering Materials. New York: John Wiley & Sons, 1996 18 Frost H J, Ashby MF. Deformation-Mechanism Maps The Plasticity and Creep of Metals and Ceramics. New York: Pergamon Press, 1982