Low cycle fatigue and fatigue crack growth behaviour of Sn-Ag

Low cycle fatigue and fatigue crack growth behaviour of Sn– Ag eutectic solder C. Kanchanomai Department of Mechanical Engineering, Nagaok a University of Technology, Nagaok a, Japan Present address: Department of Mechanical Engineering, Thammasat University (Rangsit Campus), Thailand Y. Miyashita Department of Mechanical Engineering, Nagaok a University of Technology, Nagaok a, Japan Y. Mutoh Department of Mechanical Engineering, Nagaok a University of Technology, Nagaok a, Japan S. L. Mannan Indira Gandhi Centre for Atomic Research, Tamil Nadu, India

Keywords

Fatigue, Alloys, Lead-free soldering

Abstract

Low cycle fatigue tests on as-cast Sn – Ag eutectic solder (96.5Sn– 3.5Ag) w ere carried out using a non-contact strain controlled system at 208 C with different frequencies (102 3 – 1 Hz). Steps at the boundaries of Sn-dendrites were found to be the initiation sites for microcracks in the case of low frequency fatigue tests, while for high frequency tests, crack s predominantly initiated at the boundaries of subgrains formed within Sn-dendrites. The link up of these cracks and the propagation of cracks inside the specimen occurred both transgranularly through Sn – Ag eutectic phases, and intergranularly along Sndendrit e boundaries and/ or subgrain boundaries. Propagation of stage II cracks for various frequencies could be characterized by the C*-parameter.

Received: April 2002 Accepted: June 2002

Soldering and Surface Mount Technology 14/ 3 [2002] 30–36 q MCB UP Limited

[ISSN 0954-0911] [DOI: 10.1108/09540910210444700]

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Introduction

Materials and experimental procedures

In the surface mounting technology (SMT) developed for electronic packaging , the devices are directly soldered to pads on both sides of a printed wiring board (PWB). This technology allows placement of more surface mount component s (SMC) within smaller PWB areas. However for SMT, the ability to ex and absorb thermal and mechanical strains is decreased. The thermal strain is induced by the mismatch of thermal expansion coef cient between component s during processing and in service. Since the solder is softer than other components , most of the cyclic stress and strain take place within the solder. Therefore, fatigue failure, especially thermally induced low-cycle fatigue (LCF) failure, is likely to occur in the solder. There are environmental and health concerns over the lead contained in conventional solder materials (Abtew and Selvaduray, 2000). Lead-free Sn– Ag system solders are candidates for SMT in the next generation. Therefore, understandin g of low cycle fatigue behaviour and mechanisms for lead-free solders is necessary for developing reliable SMT electronic packaging . The fatigue life of Sn– 3.5Ag – Bi solders with 2, 5 and 10 mass per cent of Bi for a total axial strain-controlled test has been shown to be dominated by true fracture ductility, which can be represented by a ductility-modi ed Cof n – Manson relationship (Kariya and Otsuka, 1998). The fatigue life of 96.5Sn – 3.5Ag is generally longer than that of 60Sn/40Pb solder for total shear strain-controlled fatigue tests at 358 C and 150 8 C (Solomon, 1991). The grain boundaries of tinrich phases are weak spots for cracking in low cycle fatigue testing of 95Sn/5Ag (Liang et al., 1996). However, only a limited number of reports are available, and the effects of frequency on LCF characteristics and mechanisms of leadfree solders are not yet fully understood . In the present study, the in uence of frequency on the LCF and fatigue crack growth (FCG) behaviour of Sn– Ag eutectic solder (96.5Sn – 3.5Ag) were investigated. To avoid the local deformation and stress concentration induced at the contact points between extensometer probes and the specimen surface, a non-contact displacement measurement system was used in these strain-controlled fatigue tests. The crack initiation and propagation mechanisms in Sn– Ag eutectic solder, thus could be observed without complication from stress concentrations at contact points.

Sn– Ag eutectic alloy (96.5Sn – 3.5Ag), which was supplied in as-solidi ed form, was used in the present study. In order to avoid the aging effect as a variable, the materials were left to fully age at room temperature for more than 60 days. The fatigue life has been shown to increase after a day or two of aging and then level off after a week (Cutiongco et al., 1990). To reveal the microstructure, the solder was etched using an etchant comprising of 10 g of FeCl3 , 2 mL of HCl and 100 mL of water. Scanning Electron Microscope (SEM) micrographs of the Sn– Ag eutectic alloy are shown in Figure 1. In the Sn– Ag eutectic alloy, the b -Sn phase is the major phase, and comprises over 90 per cent of the material by volume. The microstructure can be characterized by primary b -Sn dendrites (dark) and Sn– Ag eutectic structures (light). In the high magni cation micrograph, some needles and particles of Ag3 Sn can be observed in the Sn– Ag eutectic phase. Monotonic tensile tests were conducted at 208 C up to a small strain (about 0.03 per cent 2 strain) with a strain rate of 10 2 /s. The resultant modulus of elasticity was 50 GPa and the hardness obtained in this study was 11.5– 12 HV. The melting temperature of 96.5Sn – 3.5Ag is 2218 C (Smith and Kubalak, 1979). From the bulk solder bar materials, fatigue specimens were machined on an NC lathe. The con guration of the specimen, which was designed according to the ASTM recommendatio n (ASTM E606, 1998), has a diameter of 12 mm at the two ends, a centre diameter of 6 mm, and a gage length of 8 mm. In order to remove the deformed surface layer due to the machining process from the specimen surface, the gage part of specimen was electrolytically polished and left to fully age at room temperature again for more than 30 days. This electrolytic polishing was done at room temperature at 8 V-DC for 3 min in a solution of ethanol (80 per cent) 800 ml, distilled water 140 ml and perchloric acid (60 per cent) 60 ml. The total strain controlled fatigue tests were performed by using a servo-hydrauli c fatigue machine (Shimadzu model: EHF-F1) with a 2 kN load cell under 55 per cent relative humidity and a constant temperature of 208 C, which corresponde d to 0.64 T/Tm . A triangular strain waveform with frequencies in the range 2 10 3 – 1 Hz, 0.5 – 2 per cent total strain ranges, and R = 2 1 strain ratio were used for the fatigue tests. The test cycle commenced with a tensile load. Fatigue failure was de ned as a 25 per cent reduction in the maximum tensile load. In order to avoid any local deformation and stress concentration at the contact points which may be induced by a conventional displacement-measurin g device, a digital image measurement system was used in the present strain-

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C. Kanchanomai, Y. Miyashita, Y . Mutoh and S. L. Mannan Low cycle fatigue and fatigue crack growth behaviour of Sn– Ag eutectic solder Soldering and Surface Mount Technology 14/ 3 [2002] 30–36

Figure 1 Microstructure of Sn –Ag eutectic alloy (96.5Sn – 3.5Ag), (a) low magnication, and (b) high magnication

Figure 2 Hysteresis loops for the rst loading cycle of 96.5Sn –3.5Ag tested at 208 C

is the fatigue ductility exponent and y is the fatigue ductility coef cient. The relationship between the plastic strain range and the fatigue life for 96.5Sn – 3.5Ag solder for different frequencies is shown in Figure 3. It is seen that the fatigue ductility exponents for different frequencies are basically similar, while the fatigue ductility coef cients increase with increasing frequency. The observation of different fatigue ductility coef cients at different frequencies points to the fact that the fatigue life under these conditions is not purely cycle dependent .

Time to failure-strain relationship

controlled fatigue tests. Using a 50-mm CCD camera lens and 200-mm working distance (distance between the specimen and the lens), the eld of observation is approximately 10 mm in the longitudinal direction of the specimen, thus enabling observation of the complete gage length applied. The smallest displacement that this system can detect is 8 m m. More details about this non-contac t digital image measurement system have been given elsewhere (Kanchanoma i et al., 2002b). While running the LCF tests, the load, displacement and time were simultaneously recorded 100 times in each cycle with computer-controlle d data acquisition. In an SEM, replica lms and longitudinal cross-section of specimens were examined to study the mechanisms of crack initiation and propagation.

For high homologou s temperature conditions (approximately 0.6 T/Tm for 96.5Sn –3.5Ag), it is known that creep could occur during fatigue tests. Therefore, the relationships between stress range and total strain rate, determined from strain range and frequency of triangular waveform fatigue tests, for different strain ranges are plotted in Figure 4. It was found that the stress range increases with increasing strain rate, and the results for different total strain ranges and frequencies could be tted by a single line. This relationship can be written in a form of equation Çe T = cDs n

( 2)

where c and n are constants. The stress range exponent (n ) is approximately 18 for the present work, which is high compared to the creep exponent found in other studies, e.g. a gure of 11.2 was determined by Mavoori et al. (1997). This difference could arise from the fact that the creep exponent presented by Mavoori et al. (1997) was obtained for a constant loading condition and steady-state creep rate, while cyclic loading and constant strain rate are the case for the LCF tests reported here. For life prediction purposes, the relationship between time to failure and strain rate is also plotted in Figure 5. The

Results and discussion Cyclic stress± strain relationships The stress– strain hysteresis loops for the rst loading cycle were plotted, as shown in Figure 2, and used for determining the plastic strain range (De p ) by subtracting elastic strain range (De e ) from total strain range (De T ). This plastic strain range is equivalent to the width of the hysteresis loop and was constant during the fatigue tests. The thermally activated processes of 96.5Sn –3.5Ag (Kanchanomai et al., 2002a) could be more signi cant in low frequency tests, and this is the reason for the increasing of plastic strain range and the decreasing of stress range with decreasing frequency.

Figure 3 Relationship betw een plastic strain range and number of cycles to failure for various frequencies

Strain-life curves It is well known that the relationship between plastic strain range and the number of cycles to failure follows the Cof n – Manson equation (Cof n, 1954; Manson, 1953) De p N af = y

( 1)

where De p is the plastic strain range, Nf is the fatigue life, a

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C. Kanchanomai, Y . Miyashita, Y . Mutoh and S. L. Mannan Low cycle fatigue and fatigue crack growth behaviour of Sn –A g eutectic solder Soldering and Surface Mount Technology 14/ 3 [2002] 30–36

Figure 4 Relationship between stress range and strain rate for various total strain ranges

Figure 6 Comparison between ex perimental and predicted number of cycles to failure

time to failure decreases with increasing strain rate and all data points for various strain ranges and frequencies are located on a single line, i.e.

strain ranges and frequencies can be obtained from a single curve between time to failure and strain rate, i.e. Figure 5, while multiple fatigue life-frequency curves for each total strain range are needed for the case of a frequency-modi ed Cof n –Manson relationship. Therefore, time to failurestrain rate relationship gives good accuracy and convenience for LCF life prediction for Sn– Ag eutectic solder.

tf = c Çe m T

( 3)

where c is a constant and m is the strain rate exponent (approximately 2 0.83). From equation (3), the time to failure for the fatigue specimens can be predicted. However, time to failure and strain rate are not the common parameters for the case of LCF tests. Therefore, time to failure and strain rate can be rewritten as tf =

Nf n

Çe T = 2De T n

( 4) ( 5)

where n is frequency. Substituting equations (4) and (5) into equation (3), the following relationship can be obtained m+ 1 N f = c De m Tn

( 6)

where c is a constant. The predicted numbers of cycles to failure obtained from the time to failure-strain rate relationship (equation (6)) are given in Figure 6 together with the experimental results. The dashed lines indicate deviation from experimental results by a factor of 2. The predicted values agree well with the experimental results. It should be noted that the time to failure-strain rate relationship is different from a frequency-modi ed Cof n – Manson relationship, which has been applied to Sn– Pb eutectic solder (Shi et al., 2000). The total strain range was used instead of the plastic strain range in the case of the time to failure-strain rate relationship. Therefore, the complication from plastic strain range determination can be avoided. Moreover, the strain rate exponent (m ) for different Figure 5 Relationship between time to failure and strain rate for various frequencies

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Mechanisms of crack initiation and propagation Initiation of cracks on the surface of the test specimens was observed by a replication technique. SEM micrographs of replicas of the surface of the specimens tested at 1 per cent De T , 10 2 3 and 1 Hz are shown in Figure 7. It should be noted that the replica lm shows a reverse image of the specimen surface, i.e. a crack is represented by a n on the Figure 7 Replica lms of the surface of specimen tested at 1 per cent De T : (a) 102 3 Hz, 600 cycles, and (b) 1 Hz, 800 cycles (load direction is vertical)


2

replica lm: for the lower test frequency of 10 3 Hz, some surface cracks were observed at the interphase boundaries between Sn-dendrites (area A) and Sn– Ag eutectic phases (area B). However, the initiation of cracks was observed in the Sn-denderites (area A) for the higher test frequency of 1 Hz. For both cases, cracks were isolated at this initiation stage, although linkage to form larger cracks was seen in a few locations. Scratches in the loading direction were made on the surface of specimens before the fatigue test in order to facilitate observation of boundary sliding behaviour. However, no evidence of boundary sliding could be detected at the dendrite boundaries. It is known that grain boundar y sliding is dif cult in the material which has a dendritic microstructure (Kim and Earthman, 1994) and intermetallic particles along the grain boundary (Gabrielli and Lupinc, 1979). Therefore, it is not surprising that the sliding process is not the dominant mechanism for the Sn– Ag eutectic solder studied. However, the differences in deformation between Sn-rich phases and Sn– Ag eutectic phases can freely appear on the surface of the specimen and show steplike patterns along the boundaries. The stress intensity increases at these boundary steps, and results in the initiation of cracks during low frequency LCF. Examination of longitudinal cross-sections of tested specimens revealed formation of subgrains (approximatel y 5– 20 m m) in the Sn-dendrite phase for both low and high frequencies. The incidence of subgrains was much more prominent at high test frequencies. Evidence of these subgrains is shown in Figure 8, which should be compared with the microstructure of the specimen before fatigue testing (Figure 1), where subgrains cannot be found. The small grains observed in this study probably resulted from polygonization (rearranging the dislocations into low-strain energy subgrains) rather than recrystallization (recrystallizing into new strain-free grains) (Kanchanoma i et al., 2002a). Under high frequency loading, dislocation accumulation could be more signi cant compared to low frequency tests and this probably is the reason for the more extensive formation of subgrains in high frequency tests and also account s for the observation of initiation of surface cracks at the boundaries of subgrains in comparison to steps between Sn-dendrites and Sn– Ag eutectic phases for low frequency test conditions. Since many crack initiation sites are available in the present material, multiple cracks were formed during the LCF tests. With increasing number of cycles, the number of cracks on the specimen surface increased, however, their sizes were limited to the size of the Sn-dendrite boundaries. After a certain number of cycles, some of the surface cracks linked up to form larger cracks. In the depth direction, some of these linked up cracks propagated through the Sndendrites and became arrested at the Sn– Ag eutectic boundary, while others propagated across these boundaries and become propagating cracks (Figure 9). Link up of the

Figure 9 Longitudinal cross-section of specimen tested at 1 per cent De T , 1 Hz: intergranular along Sn-dendrite boundary (arrow A), intergranular along subgrain boundary (arrow B), and transgranular through Sn – Ag eutectic phase (arrow C) (load direction is vertical)

surface cracks and propagated cracks involved both transgranular (through Sn–Ag eutectic phases) and intergranular (along Sn-dendrite boundaries and/or subgrain boundaries) processes in both high frequency and low frequency tests.

Crack propagation curve As the cracks propagat e inside the specimen, the loadbearing area decreases (Solomon, 1985; Guo et al., 1991). Therefore, the load which is required to maintain a constant total strain range decreases with increasing number of cycles. The pattern of load reduction can be exhibited by a load drop parameter. This parameter is represented in the following form of equation f = 12

where f is the load drop parameter, DP is the load range, and DPm is the maximum load range. The maximum load range was observed at the beginning of each test. The relationship between load drop parameter and number of cycles in 96.5Sn – 3.5Ag is shown in Figure 10. The load drop parameter curves can be divided into three stages: rapid increase stage, steady-state stage and an acceleration stage. The steady-state stage dominated the fatigue life. Therefore, the slope of the load drop parameter curve in the steady-state stage re ects the LCF life and the fatigue life is longer for a atter slope during this steady-state stage. As a rst order of approximation, the relationship between the load drop parameter and the cracked area can be expressed by the following form of equation 12

Figure 8 Subgrains observed on longitudinal cross-section of the specimen tested at 1 per cent De T , 1 Hz (load direction is vertical)

( 7)

(D P DPm )

( 8)

(DP D Pm ) = Ac A0

Figure 10 Relationship between load drop parameter and number of cycles

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where Ac is the cracked area and A0 is the nominal crosssectional area. The load range decreases with increasing crack area. Since a number of surface cracks formed and then linked-up around the specimen, the assumption of a circumferential crack was made in the present study. A schematic of cracked area (Ac ) and average crack length (ac ) for a linked-up circumferential crack is shown in Figure 11. The relationship between cracked area (Ac ) and average crack length (ac ) can be given as, Ac = p ac ( 2r 2

ac )

Figure 12 Relationship between crack growth rate and DJ in the steadystate crack growth region for various frequencies

( 9)

where r is the radius of the specimen cross-section. From the steady-state stage of the load drop parameter curve (Figure 10), the cracked area can be estimated (equation (8)), which then can be used to determine the average crack length (equation (9)) for any number of cycles. Since the present fatigue tests were performed in the fully plastic region, the stress was distributed uniformly along the uncracked portion of the specimen. For a fully plastic case, a J-integral can be used to represent the intensity of the elastoplastic stress and strain eld around the crack tip. In the present work, the J-integral was estimated by using the simpli ed J-evaluation method (Miura et al., 2000; Shimakawa et al., 2000). During the present strain-controlled tension-compressio n loading, crack opening only in the tensile side was observed, therefore, it can be assumed that only the tensile loading part of the cycle in uences the crack growth behaviour. Average values of crack growth rate (dac /dN ) and the average values of DJ for different frequencies are plotted in Figure 12. Previous FCG results (Zhao et al., 2001) for a CT-specimen under a stress ratio of 0.1, a frequency of 1 Hz and a constant temperature of 208 C was compared with the present results. It was found that the plots for all frequencies tested locate 2 2 into two groups, low frequency (10 3 and 10 2 Hz) and 2 high frequency (10 1 and 1 Hz). FCG rates are higher for lower test frequencies. This increase in the crack growth rate can be explained by higher time-dependen t effects at low frequency. The exponent of the FCG plot is basically similar to that for LCF at high frequency, however, higher crack growth rates can be observed for the LCF plot. The difference is reasonable, since fully plastic conditions prevailed for the case of the LCF tests, while the plastic zone was limited in the area ahead of crack tip for the case of FCG. Since the temperature studied is well above half of the absolute melting point of 96.5Sn – 3.5Ag, the contribution of creep is signi cant and becomes the principal cause of failure. It is therefore expected that specimens would fail by the accumulation of damage due to creep-fatigue interaction. It is known that the C*-parameter is a suitable parameter for describing the crack growth rate in the

Figure 11 Schematic of cracked area (A c ) and average crack length (ac ) for a circumferential crack

creep-fatigue regime as well as in the creep regime. As a path independent line integral, the C*-parameter can be simply modi ed from the J-integral where strain and displacement are replaced by their rates (Landes and Begley, 1979; Ohji et al., 1976; Nikbin et al., 1976). Normally the J-integral is de ned as the potential energy difference between two identically loaded bodies having incrementally different crack lengths J = 2 dU da

( 10)

where U is the potential energy and a is the crack length. C* can be calculated in a similar manner using a power rate interpretation, i.e. C* is the power difference between two identically loaded bodies having incrementally different crack lengths C* = 2 dU* da

( 11)

where U* is the power or energy rate. For the case of multiple LCF specimens tested at different frequencies, the method for calculating the C*-parameter is shown in Figure 13. In Step 1, the data are collected as load versus displacement, i.e. a hysteresis loop. Since the present LCF test is in the fully plastic condition, it can be assumed that only the tensile part of the cycle in uences the crack propagation . Therefore, the energy dissipated during crack propagation can be measured as the shadow area of the hysteresis loop. Next, in Step 2, the relationship between energy and time is obtained. The slope of the energy versus time plot is the energy rate (U*). The C*-parameter, as de ned in equation (11), can be calculated from the slope of the plot between energy rate and crack length (Step 3). Relationships between crack growth rate (dac /dt ) and C* for different frequencies, obtained according to this procedure, are shown in Figure 14. It should be noted that each point on the plot represents a single specimen. The results for different frequencies locate within a narrow band with an exponent of 1, which demonstrated that the C*-parameter could be used to correlate the LCF crack growth rate for 96.5Sn – 3.5Ag in the 2 2 frequency range of 10 3 – 10 1 Hz.

Conclusions The effect of frequency on isothermal LCF and FCG behaviour of Sn– Ag eutectic (96.5Sn – 3.5Ag) solder have been studied at a constant temperature of 208 C. The main conclusions obtained are summarized as follows: (1) The LCF behaviour in the frequency range of 2 10 3 – 1 Hz followed the Cof n– Manson equation. The fatigue ductility exponents were basically similar. However, fatigue ductility coef cients were affected by frequency. A time to failure-strain rate relationship

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Figure 13 Schematic show ing four steps involved in C* data reduction

Figure 14 Relationship between crack growth rate and C* for various frequencies

(2)

(3)

The authors would like to thank T. Ori, Oki Electric Industry Co., Ltd for supplying the solder materials used in this work.

successfully described the fatigue behaviour with frequency effects. Multiple surface cracks predominantl y initiated in an intergranular manner along the boundary steps of Sndendrites for low frequency tests, and along the boundaries of subgrains in Sn-dendrites for high frequency tests. The link up of surface cracks and the propagation of cracks inside the specimen occurred both transgranularl y through the Sn– Ag eutectic phases, and intergranularly along Sn-dendrite boundaries and/or subgrain boundaries. Based on an assumption of a circumferential crack, the relationship between dac dN estimated from the load drop parameter curve in the steady-state stage, and DJ estimated using a simpli ed J-evaluation method, was obtained. The plots for all frequencies tested locate 2 2 into two groups; low frequency (10 3 and 10 2 Hz) 2 and high frequency (10 1 and 1 Hz). FCG rates are higher for the case of low frequencies. On the other hand, results for dac dt and C* for various frequencies locate within a narrow band with an exponent of 1, which demonstrated that the C*-parameter could be used to correlate the LCF crack growth rate of 96.5Sn – 3.5Ag in the frequency range of 2 2 10 3 – 10 1 Hz.

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