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Strain-rate effects on low cycle fatigue mechanism of eutectic Sn–Pb solder
International Journal of Fatigue 24 (2002) 987–993 www.elsevier.com/locate/ijfatigue
Strain-rate effects on low cycle fatigue mechanism of eutectic Sn–Pb solder C. Kanchanomai, Y. Miyashita, Y. Mutoh * Department of Mechanical Engineering, Nagaoka University of Technology, 1603-1 Kamitomioka, Nagaoka 940-2188, Japan Received 17 August 2001; received in revised form 21 November 2001; accepted 22 November 2001
Abstract Low cycle fatigue tests of as-casted Sn–Pb eutectic solder (63Sn/37Pb) were carried out using the non-contact strain-controlled system at 20°C in order to avoid local deformation and stress concentration at contact points between the extensometer and the specimen surface. The fatigue mechanisms were studied by SEM examination of polished surface of specimens and fracture surfaces. Wedge cracking due to grain boundary sliding was the dominant mechanism in the low strain rate regime, while extensive cavitation was observed on the colony boundaries at high strain rate regime. An estimation of the transition strain rate for grain boundary cracking due to sliding (e˙ ∗w) yielded a value lowers than that of the experimental result by 2–3 orders of magnitude. Relationship between time to failure and strain rate for the present results and the reported results could be expressed by a double-linear curve with the transition strain rate of approximately 10⫺3 s⫺1. 2002 Elsevier Science Ltd. All rights reserved. Keywords: Low cycle fatigue; Grain boundary sliding; Wedge crack; Cavity; Solder material; 63Sn/37Pb
1. Introduction Eutectic Sn–Pb solders have been widely used for electrical joints because of their low melting points, good wettability, good plasticity, reasonable electrical conductivity [1]. Due to their low melting temperature, the room temperature corresponds to a high homologous temperature (⬎0.5). In high homologous condition, time-dependent mechanisms, e.g. grain boundary sliding, cavitation and phase transformation, are possible to occur. These damage processes lead to premature failure when compared to cyclic-dependent fatigue failure. Shi et al. [2] found that the decrease in low cycle fatigue life of bulk 63Sn/37Pb with decreasing frequency was small at the frequencies ranging from 1 to 10⫺3 Hz but became large at the lower frequencies ranged from 10⫺3 to 10⫺4 Hz. Lee and Stone [3] found that grain boundary sliding took place at strain rates below 10⫺3 s⫺1 (s⬍40 MPa) and caused the initiation of intergranular cracks on the free surface of 63Sn/37Pb tensile-test specimens. For fatigue test [4], they found that intergranular fracture * Corresponding author. Tel.: +81-258-47-9735; fax: +81-258-479770. E-mail address: [email protected] (Y. Mutoh).
dominated at a low frequency (2×10⫺3 s⫺1), while transgranular failure dominated at a high frequency (0.1 s⫺1). Vaynman et al. [5] observed two isothermal fatigue processes in bulk 96.5Pb/3.5Sn. At a frequency of 0.2 Hz and plastic strains below approximately 0.3%, the failure mode was found to be intergranular, while mixed transgranular–intergranular was observed at higher strains. Solomon [6] found that the influence of frequency on fatigue life of 60Sn/40Pb solder could be described by a time-modified strain range partitioning approach. Raman and Reiley [7] have demonstrated the initiation of fatigue cracks due to grain boundary sliding for solid solution Sn–Pb alloys. The dependence of the intergranular failure on atmosphere for Pb-rich alloys has been reported by Berriche et al. [8]. However, a limited amount of work had been done for the influence of strain rate on fatigue mechanisms of solders. In this paper, the influence of strain rate on the isothermal low cycle fatigue (LCF) mechanism of 63Sn/37Pb solders is investigated. Based on the fatigue mechanism, relationship between time to failure and strain rate is used for lifetime prediction. The isothermal LCF results of Shi et al. [2], Cutiongco et al. [9], Guo et al. [10] are used together with the present results in the lifetime prediction.
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2. Materials and experimental procedures Sn–Pb eutectic alloy (63Sn/37Pb), which was supplied in as-casted form, was used in the present study. In order to avoid the aging effect, the material was left to fully age at room temperature for more than 60 days. The results of Cutiongco et al. [9] indicated that the fatigue life increased after a day or two of aging and leveled off after a week. The microstructure of 63Sn/37Pb, as shown in Fig. 1, consists of eutectic colonies with lamellae of Pb (light) and β–Sn (dark). By means of the linear intercept method, an average colony size is approx. 160 µm. The colony boundary behaves in a similar manner to the grain boundary; therefore ‘grain boundary’ was used for describing the behavior of the colony boundary. A monotonic tensile test at 20°C was conducted up to a strain of 0.03% under a strain rate of 10⫺2 s⫺1. The resultant modulus of elasticity, yield stress, tensile strength and elongation were 32 GPa, 18.1 MPa, 39.7 MPa and 38.1%, respectively. The hardness also obtained in this study was 11.8–12.9 HV. The melting temperature of 63Sn/37Pb solder is 183°C [11].
Fig. 1. SEM micrographs of eutectic Sn–Pb solder, (a) eutectic colonies at low magnification (b) Pb phases in β–Sn matrix at high magnification.
From bulk solder bar materials, the fatigue specimens were machined on an NC lathe machine. The fatigue specimens, which were designed according to the ASTM recommendation [12], have a gage diameter of 6 mm, and a gage length of 9 mm with a radius of curvature of 20 mm to prevent any stress concentration due to sharp corners, as shown in Fig. 2. In order to remove the deformed layer due to machining from the specimen surface, the specimen gage part 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 with 8 DC-voltage for 3 min in a solution of ethanol (80%) 800 ml, distilled water 140 ml and perchloric acid (60%) 60 ml. The total strain controlled fatigue tests were performed by using a servohydraulic fatigue machine (Shimadzu model: EHF-F1) with a 2 kN load cell under 55% relative humidity and a constant temperature of 20°C. At a test temperature of 20°C the homologous temperature of the material is 0.64. A triangular waveform with 10⫺5–4×10⫺2 s⫺1 strain rates and R ⫽ ⫺1 strain ratio was used for the fatigue tests. The cyclic loading was begun from the tensile side. The fatigue failure was defined as a 25% reduction of maximum tensile load. During fatigue testing under 2% total strain range and 4×10⫺2 s⫺1 strain rate, the temperature of the specimen was measured with a thermocouple to detect any temperature change due to self-heating. No temperature change was observed at an accuracy of 0.1°C. In order to avoid the local deformation and stress concentration at the contact point induced by the conventional displacement-measuring device, the digital image measurement system was used in the present strain-controlled fatigue test. Details of the non-contact digital image measurement system are contained in a previous report [13]. During the test, the load, displacement and time were simultaneously recorded 100 times in each cycle with personal computer-controlled data acquisition. The hysteresis loops, an example of which are shown in Fig. 3, were plotted and used for determining plastic strain by subtracting elastic strain from total strain (width of hysteresis loop). After failure, the pol-
Fig. 2. Low cycle fatigue specimen geometry (dimension in mm).
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Fig. 3. Hysteresis loop of eutectic Sn–Pb solder tested at 2%⌬⑀T, 4×10⫺5 s⫺1 strain rate.
ished specimen surfaces and fracture surfaces of the specimens were examined in an SEM.
3. Results and discussion 3.1. Low cycle fatigue behavior and mechanisms The relationships between the number of cycles to failure (Nf) and strain rate are shown in Fig. 4. The reduction in the number of cycles to failure with decreasing strain rate can be observed for both 0.5% and 2% total strain ranges (⌬⑀T). Two dashed straight lines, which showed almost the same slopes for both high and low strain rate regimes were drawn for each curve to emphasize the transition regime at some intermediate strain rates (10⫺4–10⫺3 s⫺1). This transition behavior
Fig. 4. Relationship between the number of cycles to failure (Nf) and strain rate (e˙ ).
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reflects the differences in fatigue mechanisms between the two regimes. The effect of strain rate on fatigue life was more significant at low strain range compared to high strain range. Similar behavior has been reported for a Cr–Mo–V steel [14]. For high homologous temperature LCF condition (approx. 0.64 T/Tm for 63Sn/37Pb in the present study), it is known that the time-dependent deformation (creep) is likely to occur together with fatigue, i.e. creep–fatigue interaction. Creep failure is characterized by intergranular cracking due to grain boundary sliding, while fatigue failure occurs due to formation of surface cracks and then propagation. The creep–fatigue failure can be viewed as an interaction between grain boundary cracks and fatigue cracks. As the contribution from grain boundary sliding is expected to increase with the decrease in strain rates, creep–fatigue interaction would assume greater significance at lower strain rates. Therefore, failure would be intragranular at high frequencies and become intergranular at low frequencies due to grain boundary sliding [15]. In order to characterize the effect of strain rate on the LCF mechanism, the surfaces of the specimens tested at 2%⌬⑀T for strain rates of 4×10⫺5 and 4×10⫺2 s⫺1 were polished and observed by using an SEM, as shown in Fig. 5. The micrograph of the 4×10⫺5 s⫺1 strain rate specimen represents the LCF mechanism observed for low strain rate tests, while that of 4×10⫺2 s⫺1 strain rate represents the LCF mechanism observed for high strain rate tests. Cavities on colony boundaries and wedge cracks around the triple-point of the grain junction can be seen for the specimens tested at low strain rates, while only cavities on the colony boundaries can be observed for the specimens tested at high strain rates. The wedge cracks nucleated ahead of the crack tip can accelerate fatigue crack propagation and result in shorter fatigue life. For high strain rate fatigue tests, the deformation of grain matrix without grain boundary sliding controls flow behavior. The fatigue crack propagation without grain boundary sliding at high strain rate is slower and consequently results in longer fatigue life (Fig. 4). From fracture surface observation, cavities were observed along the colony boundary, especially on the interphases between Sn-rich (dark) and Pb-rich (light) phases for both low and high strain rate tests. The cavity size was approx. 0.5–2 µm. Examples of fracture surfaces and cavities are shown in Fig. 6. Both fracture surfaces tested at high and low strain rates showed intergranular fracture. However, intergranular fractures were more dominant at lower strain rates as the contribution from grain boundary sliding increased. There are two main theoretical explanations for cavitation on grain boundary at elevated temperature. One is an extension of the low-temperature mechanism for the nucleation of voids at grain boundary ledges (the intersection between slip band and grain boundary), or second phase particles
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Fig. 5. SEM micrographs of polished surface of eutectic Sn–Pb solder specimens tested at 2%⌬⑀T, (a) low strain rate (4×10⫺5 s⫺1) and (b) high strain rate (4×10⫺2 s⫺1) (load direction in vertical).
[16]. This nucleation is controlled by the build-up of internal stresses (local dislocation concentration) around grain boundary ledges or particles as a result of incomplete plastic relaxation. This grain boundary cavitation appears more readily under the condition of grain boundary sliding. The second mechanism invokes the clustering of vacancies to form (by diffusion) a void cluster [17]. The model describing this mechanism predicts that (a) cavities are most probably formed at second-phase particles on the grain boundary; (b) they can be formed even when the normal stress at the particle–matrix interface is smaller than the theoretical fracture strength of the interface; (c) the probability of cavity nucleation is the highest at the perimeter of contact between the particle and the grain boundary; and (d) in addition to a threshold stress, an incubation time must elapse before enough vacancies can cluster together (by diffusion) to form a void of critical size. In the present study, the first viewpoint dealing with the extension of the low temperature mechanism for the nucleation of void seems to be operative. At high strain rates, stress concentration at the interphase boundaries between Sn-rich and Pb-rich
phases due to blockage of slip would lead to the formation of cavities, while at low strain rates, grain boundary sliding also contributes to the formation of cavities as evidenced by the observation of wedge cracks (Fig. 5). Relationships between maximum nominal stresses, plastic strain ranges (width of hysteresis loop) and strain rates are shown in Fig. 7. The dependence of maximum nominal stress on strain rate (strain-rate sensitivity of maximum nominal stress, dlns / dlne˙ ) and the dependence of plastic strain range on strain rate (strain-rate sensitivity of plastic strain range, dln⌬ep / dlne˙ ) are stronger in the low strain rates (approx. 10⫺5–10⫺3 s⫺1) and become weaker at high strain rates. Both the maximum nominal stress versus strain rate, and the plastic strain range versus strain rate diagrams show a transition at some intermediate strain rates (approx. 10⫺3 s⫺1). This transition range of strain rate also coincides with the transition range of strain rate shown in Fig. 4, where the dominant deformation mechanism changes from the matrix deformation without grain boundary sliding at high strain rates to the matrix deformation with grain boundary sliding at low strain rates. According to the model proposed by Hart [18], the time-dependent deformation can be regarded as a non-Newtonian body for power-law behavior of the matrix and Newtonian flow for linear shear sliding of the grain boundary. For polycrystals like a solder studied here, the deformation induced by sliding at the grain boundary and the continuous deformation of the matrix are compatible. In the low strain rates, the grain boundaries have less shear resistance; therefore the deformation occurred becuase of a mixture of grain boundary sliding and matrix deformation. On the other hand, the grain boundaries have higher shear resistance and are strong enough to prevent any sliding in the high strain rates. For a non-Newtonian body (power-law behavior of the matrix), the flow stress rises with increasing strain rate less rapidly than that of Newtonian flow. This behavior results in low strain-rate sensitivity (dlns / dlne˙ ) in the high strain rates. Assuming a linear shear resistance for the grain boundary and a power law behavior for the matrix, Baik and Raj [19] have proposed a model for the estimation of an upper bound strain rate for wedge cracking (e˙ ∗w) as follows: Y⍀ dDb e˙ w∗ ⫽ 0.27 kT (p / l)2Lp2
(1)
where Y is the effective tensile yield stress of the material, ⍀ is the atomic volume, k is the Boltzman’s constant, T is the absolute temperature, p is the particle size, l is average spacing of the particle on the boundary, L is the grain size and dDb is the boundary width times the coefficient of grain boundary self diffusion. For the present work, tin is the dominant phase, therefore its atomic volume was used in this estimation and the lead-rich phases located along the colony boundaries
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Fig. 6. SEM micrographs of fracture surface of eutectic Sn–Pb solder specimens tested at 2%⌬⑀T, (a) 4×10⫺5 s⫺1 strain rate at low magnification, (b) 4×10⫺5 s⫺1 strain rate at high magnification, (c) 4×10⫺2 s⫺1 strain rate at low magnification, and (d) 4×10⫺2 s⫺1 strain rate at high magnification. Table 1 Parameters for the transition strain rate (e˙ ∗w) estimation Y ⍀ k T p l L dDb
Fig. 7. Relationships between maximum nominal stress, plastic strain range and strain rate for eutectic Sn–Pb solder tested at 0.5%⌬⑀T.
were considered as second phase particles here. Details of parameters used here are summarized in Table 1. From the estimation, the upper bound strain rate (e˙ w∗ ) occurs at approx. 10⫺6 s⫺1, while that of experimental results is in the range of 10⫺4–10⫺3 s⫺1. The difference between the estimated and experimental values may result from the difference in mechanisms of boundary sliding. The estimated value is based on the assumption of a linear shear resistance for the boundary, i.e. power exponent for grain boundary sliding of 1. However, the
Effective tensile yield stress, 18.1 MPa Atomic volume of tin, 54.1×10⫺30 m3 [20] Boltzman’s constant, 1.381×10⫺23 J K⫺1 Absolute temperature, 293 K Size of lead phase, 2–5 µm Spacing of the particle in the boundary, 5–10 µm Colony size, 160 µm Boundary width times the coefficient of grain boundary diffusion, approx. 10⫺21 m3 s⫺1 at room temperature [21]
actual shear resistance for colony boundary for eutectic Sn–Pb is probably not linear. Therefore, differences between the estimated and experimental values can possibly occur. 3.2. Lifetime prediction of low cycle fatigue A number of lifetime prediction methods have been used for LCF of eutectic Sn–Pb solder. The frequencymodified Coffin–Manson relationship has successfully related plastic strain range to frequency-modified fatigue life in the form of simple power law. This method has been applied to eutectic Sn–Pb solder [2]. Based on the stress and strain micro–macro correlations, a modified
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Fig. 8. Relationship between time to failure and strain rate for eutectic Sn–Pb solder.
Coffin–Manson lifetime relationship, proposed by Zubelewicz et al. [22], has successfully predicted fatigue lives of 63Sn/37Pb. Kuo et al. [20] have proposed a constrained cavity growth model to predict the creep–fatigue life of Sn–Pb solder. In the present study, another kind of lifetime prediction, which takes the effect of strain rate on time-dependent mechanism into account, is proposed. Since the time-dependent mechanism is the dominant mechanism for the eutectic Sn–Pb solder studied here, the relationships between time to failure (tf) and strain rate (e˙ ) for the present results and the previous reports [2,9,10] are shown in Fig. 8. The testing conditions for all data are summarized in Table 2. For all the data, strain range, testing temperature and waveform were basically similar, however failure definition, heat treatment and loading mode were different. Shi et al. [2] used the number of cycles to complete fracture as the failure
definition, while 25% reduction of maximum tensile load, which represents the transition from the steadystate crack propagation stage to the instability crack growth stage [23], was used here. Since the unstable crack growth rate is fast, the difference between time to failure based on both failure definitions would not be significant. Moreover, the objectives of heat treatment used here and that used by Shi et al. [2] are basically similar, i.e. to reduce the effect of residue stress and strain. The difference in the heat treatment, i.e. 24 h at 60°C by Shi et al. [2] and 20°C for 30 days in the present study, are not expected to introduce any significant variations in the properties of these solders [9]. The plots of both Shi et al. [2] and the present results show the decrease in time to failure with increasing strain rate and fall on the double-linear line with the transition strain rate of approx. 10⫺3 s⫺1. This transition strain rate corresponds to the transition strain rate (e˙ w∗ ), which separates two regimes of deformation: one is the matrix deformation with grain boundary sliding at low strain rates and the other is the matrix deformation without grain boundary sliding at high strain rates. The piecewise power laws obtained from data fitting are indicated in the following form: (a) At the strain rates higher than 10⫺3 s⫺1, tf ⫽ 45.15e˙ ⫺0.96
(2)
(b) At the strain rates lower than 10
⫺3
⫺1
s ,
tf ⫽ 380e˙ ⫺0.65
(3)
In the high strain rate regime, the results of Cutiongco et al. [9] and Guo et al. [10], which include the effect of loading mode (pull–pull) as compared to push–pull used in this study, are in good agreement with the present results (Fig. 8). At present, the effect of loading mode of LCF of eutectic Sn–Pb solder is still unclear. However, the difference between push–pull and pull–
Table 2 The low cycle fatigue testing conditions Materials
Strain range
Temperature
Waveform
Failure definition
63Sn/37Pb
2%⌬eT
25°C
Triangular
Separation
63Sn/37Pb
0.6–2%⌬eT
25°C
Saw-tooth
63Sn/37Pb
0.5–2%⌬eT
25°C
Saw-tooth
62Sn/37Pb
0.5–2%⌬eT
20°C
Triangular
Heat treatment
Annealed at 60°C for 24 h in a N2 atmosphere Drop-in-stress Heat treated for 2 h at ratio (smax/smin) 150°C and left in air for 6–10 days Young’s Heat treated for 2 h at modulus drop 150°C and left in air for 6–10 days 25% reduction Electrolytically of maximum polished and fully tensile load aged at room temperature for more than 30 days
Loading mode
Ref.
Symmetrical uniaxial push– pull Uniaxial pull– pull
[2]
Uniaxial pull– pull
[10]
Symmetrical uniaxial push– pull
Present work
[9]
C. Kanchanomai et al. / International Journal of Fatigue 24 (2002) 987–993
pull modes is expected to be more significant at low strain rates where time-dependent damage processes dominate. The agreement observed at high rates is, therefore, not surprising.
4. Conclusion The effect of strain rate on the isothermal LCF mechanisms of Sn–Pb eutectic (63Sn/37Pb) solder have been studied at a constant temperature of 20°C. The main conclusions obtained are summarized as follows: 1. The relationships between number of cycles to failure (Nf) and strain rate showed the S-shaped characteristics. The slopes in the low strain rate regime and the high strain rate regime were nearly identical. The effect of strain rate on fatigue life became less with increasing total strain range. Cavitation due to grain boundary sliding was the dominant failure mechanism in the low strain rate regime, while cavitation without grain boundary sliding was the dominant mechanism in the high strain rate regime. The transition strain rate was approx. 10⫺3–10⫺4 s⫺1. 2. An estimation of the upper bound strain rate (e˙ ∗w) for wedge-type fracture in LCF based on the assumption of a linear shear resistance for the grain boundary and a power law behavior for the matrix yielded a value lower than the experimental value by 2–3 orders of magnitude. Therefore, it seemed that the assumption of a linear shear resistance for the boundary may not be valid in the case of the colony boundary of eutectic Sn–Pb studied here. 3. The relationship between time to failure and strain rate for the present results was in good agreement with the reported results [2,9,10]. The time to failure decreased with increasing strain rate. The relationship could be expressed by a double-linear curve with the transition strain rate of approx. 10⫺3 s⫺1.
Acknowledgements The authors would like to thank T. Ori, Oki Electric Industry Co. Ltd for supplying solder materials used in this work. They also express sincere thanks to Dr S.L. Mannan for useful discussion.
References [1] Kang SK, Sarkhel AK. Lead (Pb)-free solders for electronic packaging. Journal of Electronic Materials 1994;23(8):701–7.
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[2] Shi XQ, Pang HLJ, Zhou W, Wang ZP. Low cycle fatigue analysis of temperature and frequency effects in eutectic solder alloy. International Journal of Fatigue 2000;22:217–28. [3] Lee SM, Stone DS. Grain boundary sliding in as-cast Pb–Sn eutectic. Scripta Metallurgica et Materialia 1994;30(9):1213–8. [4] Lee SM, Stone DS. Deformation and fracture of Pb–Sn-eutectic under tensile and fatigue loading. Journal of Electronic Packaging, Transactions of the ASME 1992;114:118–22. [5] Vaynman S, Fine ME, Jeannotte DA. Isothermal fatigue of low tin lead based solder. Metallurgical Transaction A 1988;19:1051–9. [6] Solomon HD. Creep, strain rate sensitivity and low cycle fatigue of 60/40 solder. Brazing and Soldering 1986;11:68–75. [7] Raman V, Reiley TC. Cyclic deformation and fracture in Pb–Sn solid solution alloy. Metallurgical Transactions A 1988;19:1533–46. [8] Berriche R, Fine ME, Jeannotte DA. Environmental and hold time effects on fatigue of low-tin lead-based solder. Metallurgical Transaction A 1991;22:357–66. [9] Cutiongco EC, Vaynman S, Fine ME, Jeannotte DA. Isothermal fatigue of 63Sn–37Pb solder. Journal of Electronic Packaging, Transactions of the ASME 1990;112:110–4. [10] Guo G, Cutiongco EC, Keer LM, Fine ME. Thermomechanical fatigue life prediction of 63Sn/37Pb solder. Journal of Electronic Packaging, Transactions of the ASME 1992;114:145–51. [11] Smith JF, Kubalak RR. Tin and tin alloy. In: Metals handbook, 2. Metals Park, OH: American Society for Metals; 1979. p. 613–25. [12] ASTM standards, ASTM E606: standard practice for strain-controlled fatigue testing, 03.01. American Society for Testing and Materials, 1998. p. 525–39. [13] Kanchanomai C, Yamamoto S, Miyashita Y, Mutoh Y, McEvily AJ. Low cycle fatigue test for solders using non-contact digital image measurement system. International Journal of Fatigue 2002;24:57–67. [14] Coles A, Hill GJ, Dawson RAT, Watson SJ. The high-strain fatigue properties of low-alloy creep-resisting steel. Thermal and High-Strain Fatigue: Proceedings of an International Conference organized by the Institute of Metals in association with the Iron and Steel Institute, 6–7 June 1967, London, pp. 270–94. [15] Stone DS. The creep–fatigue interaction in solders and solder joints. Journal of Electronic Packaging, Transactions of the ASME 1990;112:100–3. [16] Good SH, Brown LM. The nucleation of cavities by plastic deformation. Acta Metallurgica 1979;27:1–15. [17] Raj R, Ashby MF. Intergranular fracture at elevated temperature. Acta Metallurgica 1975;23:653–66. [18] Hart EW. A theory for flow of polycrystals. Acta Metallurgica 1967;15:1545–9. [19] Baik S, Raj R. Wedge type damage in low cycle fatigue. Metallurgical Transactions A 1982;13:1207–14. [20] Kuo CG, Sastry SML, Jerina KL. Creep–fatigue life prediction of in situ composite solders. Metallurgical and Materials Transaction A 1995;26:3265–75. [21] Kaur I, Gust W, Kozma L. Handbook of grain and interphase boundary diffusion data, vol. 2. Stuttgart: Ziegler Press, 1989. p. 1179–1217. [22] Zubelewicz A, Guo Q, Cutiongco EC, Fine ME, Keer LM. Micromechanical method to predict fatigue life of solder. Journal of Electronic Packaging, Transactions of the ASME 1990;112:179–82. [23] Kanchanomai C, Miyashita Y, Mutoh Y. Low cycle fatigue and mechanisms of a eutectic Sn–Pb solder 63Sn/37Pb. International Journal of Fatigue 2002;24(6):671–83.
Strain-rate effects on low cycle fatigue mechanism of eutectic Sn–Pb solder C. Kanchanomai, Y. Miyashita, Y. Mutoh * Department of Mechanical Engineering, Nagaoka University of Technology, 1603-1 Kamitomioka, Nagaoka 940-2188, Japan Received 17 August 2001; received in revised form 21 November 2001; accepted 22 November 2001
Abstract Low cycle fatigue tests of as-casted Sn–Pb eutectic solder (63Sn/37Pb) were carried out using the non-contact strain-controlled system at 20°C in order to avoid local deformation and stress concentration at contact points between the extensometer and the specimen surface. The fatigue mechanisms were studied by SEM examination of polished surface of specimens and fracture surfaces. Wedge cracking due to grain boundary sliding was the dominant mechanism in the low strain rate regime, while extensive cavitation was observed on the colony boundaries at high strain rate regime. An estimation of the transition strain rate for grain boundary cracking due to sliding (e˙ ∗w) yielded a value lowers than that of the experimental result by 2–3 orders of magnitude. Relationship between time to failure and strain rate for the present results and the reported results could be expressed by a double-linear curve with the transition strain rate of approximately 10⫺3 s⫺1. 2002 Elsevier Science Ltd. All rights reserved. Keywords: Low cycle fatigue; Grain boundary sliding; Wedge crack; Cavity; Solder material; 63Sn/37Pb
1. Introduction Eutectic Sn–Pb solders have been widely used for electrical joints because of their low melting points, good wettability, good plasticity, reasonable electrical conductivity [1]. Due to their low melting temperature, the room temperature corresponds to a high homologous temperature (⬎0.5). In high homologous condition, time-dependent mechanisms, e.g. grain boundary sliding, cavitation and phase transformation, are possible to occur. These damage processes lead to premature failure when compared to cyclic-dependent fatigue failure. Shi et al. [2] found that the decrease in low cycle fatigue life of bulk 63Sn/37Pb with decreasing frequency was small at the frequencies ranging from 1 to 10⫺3 Hz but became large at the lower frequencies ranged from 10⫺3 to 10⫺4 Hz. Lee and Stone [3] found that grain boundary sliding took place at strain rates below 10⫺3 s⫺1 (s⬍40 MPa) and caused the initiation of intergranular cracks on the free surface of 63Sn/37Pb tensile-test specimens. For fatigue test [4], they found that intergranular fracture * Corresponding author. Tel.: +81-258-47-9735; fax: +81-258-479770. E-mail address: [email protected] (Y. Mutoh).
dominated at a low frequency (2×10⫺3 s⫺1), while transgranular failure dominated at a high frequency (0.1 s⫺1). Vaynman et al. [5] observed two isothermal fatigue processes in bulk 96.5Pb/3.5Sn. At a frequency of 0.2 Hz and plastic strains below approximately 0.3%, the failure mode was found to be intergranular, while mixed transgranular–intergranular was observed at higher strains. Solomon [6] found that the influence of frequency on fatigue life of 60Sn/40Pb solder could be described by a time-modified strain range partitioning approach. Raman and Reiley [7] have demonstrated the initiation of fatigue cracks due to grain boundary sliding for solid solution Sn–Pb alloys. The dependence of the intergranular failure on atmosphere for Pb-rich alloys has been reported by Berriche et al. [8]. However, a limited amount of work had been done for the influence of strain rate on fatigue mechanisms of solders. In this paper, the influence of strain rate on the isothermal low cycle fatigue (LCF) mechanism of 63Sn/37Pb solders is investigated. Based on the fatigue mechanism, relationship between time to failure and strain rate is used for lifetime prediction. The isothermal LCF results of Shi et al. [2], Cutiongco et al. [9], Guo et al. [10] are used together with the present results in the lifetime prediction.
0142-1123/02/$ - see front matter 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 1 4 2 - 1 1 2 3 ( 0 2 ) 0 0 0 1 1 - 7
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2. Materials and experimental procedures Sn–Pb eutectic alloy (63Sn/37Pb), which was supplied in as-casted form, was used in the present study. In order to avoid the aging effect, the material was left to fully age at room temperature for more than 60 days. The results of Cutiongco et al. [9] indicated that the fatigue life increased after a day or two of aging and leveled off after a week. The microstructure of 63Sn/37Pb, as shown in Fig. 1, consists of eutectic colonies with lamellae of Pb (light) and β–Sn (dark). By means of the linear intercept method, an average colony size is approx. 160 µm. The colony boundary behaves in a similar manner to the grain boundary; therefore ‘grain boundary’ was used for describing the behavior of the colony boundary. A monotonic tensile test at 20°C was conducted up to a strain of 0.03% under a strain rate of 10⫺2 s⫺1. The resultant modulus of elasticity, yield stress, tensile strength and elongation were 32 GPa, 18.1 MPa, 39.7 MPa and 38.1%, respectively. The hardness also obtained in this study was 11.8–12.9 HV. The melting temperature of 63Sn/37Pb solder is 183°C [11].
Fig. 1. SEM micrographs of eutectic Sn–Pb solder, (a) eutectic colonies at low magnification (b) Pb phases in β–Sn matrix at high magnification.
From bulk solder bar materials, the fatigue specimens were machined on an NC lathe machine. The fatigue specimens, which were designed according to the ASTM recommendation [12], have a gage diameter of 6 mm, and a gage length of 9 mm with a radius of curvature of 20 mm to prevent any stress concentration due to sharp corners, as shown in Fig. 2. In order to remove the deformed layer due to machining from the specimen surface, the specimen gage part 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 with 8 DC-voltage for 3 min in a solution of ethanol (80%) 800 ml, distilled water 140 ml and perchloric acid (60%) 60 ml. The total strain controlled fatigue tests were performed by using a servohydraulic fatigue machine (Shimadzu model: EHF-F1) with a 2 kN load cell under 55% relative humidity and a constant temperature of 20°C. At a test temperature of 20°C the homologous temperature of the material is 0.64. A triangular waveform with 10⫺5–4×10⫺2 s⫺1 strain rates and R ⫽ ⫺1 strain ratio was used for the fatigue tests. The cyclic loading was begun from the tensile side. The fatigue failure was defined as a 25% reduction of maximum tensile load. During fatigue testing under 2% total strain range and 4×10⫺2 s⫺1 strain rate, the temperature of the specimen was measured with a thermocouple to detect any temperature change due to self-heating. No temperature change was observed at an accuracy of 0.1°C. In order to avoid the local deformation and stress concentration at the contact point induced by the conventional displacement-measuring device, the digital image measurement system was used in the present strain-controlled fatigue test. Details of the non-contact digital image measurement system are contained in a previous report [13]. During the test, the load, displacement and time were simultaneously recorded 100 times in each cycle with personal computer-controlled data acquisition. The hysteresis loops, an example of which are shown in Fig. 3, were plotted and used for determining plastic strain by subtracting elastic strain from total strain (width of hysteresis loop). After failure, the pol-
Fig. 2. Low cycle fatigue specimen geometry (dimension in mm).
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Fig. 3. Hysteresis loop of eutectic Sn–Pb solder tested at 2%⌬⑀T, 4×10⫺5 s⫺1 strain rate.
ished specimen surfaces and fracture surfaces of the specimens were examined in an SEM.
3. Results and discussion 3.1. Low cycle fatigue behavior and mechanisms The relationships between the number of cycles to failure (Nf) and strain rate are shown in Fig. 4. The reduction in the number of cycles to failure with decreasing strain rate can be observed for both 0.5% and 2% total strain ranges (⌬⑀T). Two dashed straight lines, which showed almost the same slopes for both high and low strain rate regimes were drawn for each curve to emphasize the transition regime at some intermediate strain rates (10⫺4–10⫺3 s⫺1). This transition behavior
Fig. 4. Relationship between the number of cycles to failure (Nf) and strain rate (e˙ ).
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reflects the differences in fatigue mechanisms between the two regimes. The effect of strain rate on fatigue life was more significant at low strain range compared to high strain range. Similar behavior has been reported for a Cr–Mo–V steel [14]. For high homologous temperature LCF condition (approx. 0.64 T/Tm for 63Sn/37Pb in the present study), it is known that the time-dependent deformation (creep) is likely to occur together with fatigue, i.e. creep–fatigue interaction. Creep failure is characterized by intergranular cracking due to grain boundary sliding, while fatigue failure occurs due to formation of surface cracks and then propagation. The creep–fatigue failure can be viewed as an interaction between grain boundary cracks and fatigue cracks. As the contribution from grain boundary sliding is expected to increase with the decrease in strain rates, creep–fatigue interaction would assume greater significance at lower strain rates. Therefore, failure would be intragranular at high frequencies and become intergranular at low frequencies due to grain boundary sliding [15]. In order to characterize the effect of strain rate on the LCF mechanism, the surfaces of the specimens tested at 2%⌬⑀T for strain rates of 4×10⫺5 and 4×10⫺2 s⫺1 were polished and observed by using an SEM, as shown in Fig. 5. The micrograph of the 4×10⫺5 s⫺1 strain rate specimen represents the LCF mechanism observed for low strain rate tests, while that of 4×10⫺2 s⫺1 strain rate represents the LCF mechanism observed for high strain rate tests. Cavities on colony boundaries and wedge cracks around the triple-point of the grain junction can be seen for the specimens tested at low strain rates, while only cavities on the colony boundaries can be observed for the specimens tested at high strain rates. The wedge cracks nucleated ahead of the crack tip can accelerate fatigue crack propagation and result in shorter fatigue life. For high strain rate fatigue tests, the deformation of grain matrix without grain boundary sliding controls flow behavior. The fatigue crack propagation without grain boundary sliding at high strain rate is slower and consequently results in longer fatigue life (Fig. 4). From fracture surface observation, cavities were observed along the colony boundary, especially on the interphases between Sn-rich (dark) and Pb-rich (light) phases for both low and high strain rate tests. The cavity size was approx. 0.5–2 µm. Examples of fracture surfaces and cavities are shown in Fig. 6. Both fracture surfaces tested at high and low strain rates showed intergranular fracture. However, intergranular fractures were more dominant at lower strain rates as the contribution from grain boundary sliding increased. There are two main theoretical explanations for cavitation on grain boundary at elevated temperature. One is an extension of the low-temperature mechanism for the nucleation of voids at grain boundary ledges (the intersection between slip band and grain boundary), or second phase particles
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Fig. 5. SEM micrographs of polished surface of eutectic Sn–Pb solder specimens tested at 2%⌬⑀T, (a) low strain rate (4×10⫺5 s⫺1) and (b) high strain rate (4×10⫺2 s⫺1) (load direction in vertical).
[16]. This nucleation is controlled by the build-up of internal stresses (local dislocation concentration) around grain boundary ledges or particles as a result of incomplete plastic relaxation. This grain boundary cavitation appears more readily under the condition of grain boundary sliding. The second mechanism invokes the clustering of vacancies to form (by diffusion) a void cluster [17]. The model describing this mechanism predicts that (a) cavities are most probably formed at second-phase particles on the grain boundary; (b) they can be formed even when the normal stress at the particle–matrix interface is smaller than the theoretical fracture strength of the interface; (c) the probability of cavity nucleation is the highest at the perimeter of contact between the particle and the grain boundary; and (d) in addition to a threshold stress, an incubation time must elapse before enough vacancies can cluster together (by diffusion) to form a void of critical size. In the present study, the first viewpoint dealing with the extension of the low temperature mechanism for the nucleation of void seems to be operative. At high strain rates, stress concentration at the interphase boundaries between Sn-rich and Pb-rich
phases due to blockage of slip would lead to the formation of cavities, while at low strain rates, grain boundary sliding also contributes to the formation of cavities as evidenced by the observation of wedge cracks (Fig. 5). Relationships between maximum nominal stresses, plastic strain ranges (width of hysteresis loop) and strain rates are shown in Fig. 7. The dependence of maximum nominal stress on strain rate (strain-rate sensitivity of maximum nominal stress, dlns / dlne˙ ) and the dependence of plastic strain range on strain rate (strain-rate sensitivity of plastic strain range, dln⌬ep / dlne˙ ) are stronger in the low strain rates (approx. 10⫺5–10⫺3 s⫺1) and become weaker at high strain rates. Both the maximum nominal stress versus strain rate, and the plastic strain range versus strain rate diagrams show a transition at some intermediate strain rates (approx. 10⫺3 s⫺1). This transition range of strain rate also coincides with the transition range of strain rate shown in Fig. 4, where the dominant deformation mechanism changes from the matrix deformation without grain boundary sliding at high strain rates to the matrix deformation with grain boundary sliding at low strain rates. According to the model proposed by Hart [18], the time-dependent deformation can be regarded as a non-Newtonian body for power-law behavior of the matrix and Newtonian flow for linear shear sliding of the grain boundary. For polycrystals like a solder studied here, the deformation induced by sliding at the grain boundary and the continuous deformation of the matrix are compatible. In the low strain rates, the grain boundaries have less shear resistance; therefore the deformation occurred becuase of a mixture of grain boundary sliding and matrix deformation. On the other hand, the grain boundaries have higher shear resistance and are strong enough to prevent any sliding in the high strain rates. For a non-Newtonian body (power-law behavior of the matrix), the flow stress rises with increasing strain rate less rapidly than that of Newtonian flow. This behavior results in low strain-rate sensitivity (dlns / dlne˙ ) in the high strain rates. Assuming a linear shear resistance for the grain boundary and a power law behavior for the matrix, Baik and Raj [19] have proposed a model for the estimation of an upper bound strain rate for wedge cracking (e˙ ∗w) as follows: Y⍀ dDb e˙ w∗ ⫽ 0.27 kT (p / l)2Lp2
(1)
where Y is the effective tensile yield stress of the material, ⍀ is the atomic volume, k is the Boltzman’s constant, T is the absolute temperature, p is the particle size, l is average spacing of the particle on the boundary, L is the grain size and dDb is the boundary width times the coefficient of grain boundary self diffusion. For the present work, tin is the dominant phase, therefore its atomic volume was used in this estimation and the lead-rich phases located along the colony boundaries
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Fig. 6. SEM micrographs of fracture surface of eutectic Sn–Pb solder specimens tested at 2%⌬⑀T, (a) 4×10⫺5 s⫺1 strain rate at low magnification, (b) 4×10⫺5 s⫺1 strain rate at high magnification, (c) 4×10⫺2 s⫺1 strain rate at low magnification, and (d) 4×10⫺2 s⫺1 strain rate at high magnification. Table 1 Parameters for the transition strain rate (e˙ ∗w) estimation Y ⍀ k T p l L dDb
Fig. 7. Relationships between maximum nominal stress, plastic strain range and strain rate for eutectic Sn–Pb solder tested at 0.5%⌬⑀T.
were considered as second phase particles here. Details of parameters used here are summarized in Table 1. From the estimation, the upper bound strain rate (e˙ w∗ ) occurs at approx. 10⫺6 s⫺1, while that of experimental results is in the range of 10⫺4–10⫺3 s⫺1. The difference between the estimated and experimental values may result from the difference in mechanisms of boundary sliding. The estimated value is based on the assumption of a linear shear resistance for the boundary, i.e. power exponent for grain boundary sliding of 1. However, the
Effective tensile yield stress, 18.1 MPa Atomic volume of tin, 54.1×10⫺30 m3 [20] Boltzman’s constant, 1.381×10⫺23 J K⫺1 Absolute temperature, 293 K Size of lead phase, 2–5 µm Spacing of the particle in the boundary, 5–10 µm Colony size, 160 µm Boundary width times the coefficient of grain boundary diffusion, approx. 10⫺21 m3 s⫺1 at room temperature [21]
actual shear resistance for colony boundary for eutectic Sn–Pb is probably not linear. Therefore, differences between the estimated and experimental values can possibly occur. 3.2. Lifetime prediction of low cycle fatigue A number of lifetime prediction methods have been used for LCF of eutectic Sn–Pb solder. The frequencymodified Coffin–Manson relationship has successfully related plastic strain range to frequency-modified fatigue life in the form of simple power law. This method has been applied to eutectic Sn–Pb solder [2]. Based on the stress and strain micro–macro correlations, a modified
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Fig. 8. Relationship between time to failure and strain rate for eutectic Sn–Pb solder.
Coffin–Manson lifetime relationship, proposed by Zubelewicz et al. [22], has successfully predicted fatigue lives of 63Sn/37Pb. Kuo et al. [20] have proposed a constrained cavity growth model to predict the creep–fatigue life of Sn–Pb solder. In the present study, another kind of lifetime prediction, which takes the effect of strain rate on time-dependent mechanism into account, is proposed. Since the time-dependent mechanism is the dominant mechanism for the eutectic Sn–Pb solder studied here, the relationships between time to failure (tf) and strain rate (e˙ ) for the present results and the previous reports [2,9,10] are shown in Fig. 8. The testing conditions for all data are summarized in Table 2. For all the data, strain range, testing temperature and waveform were basically similar, however failure definition, heat treatment and loading mode were different. Shi et al. [2] used the number of cycles to complete fracture as the failure
definition, while 25% reduction of maximum tensile load, which represents the transition from the steadystate crack propagation stage to the instability crack growth stage [23], was used here. Since the unstable crack growth rate is fast, the difference between time to failure based on both failure definitions would not be significant. Moreover, the objectives of heat treatment used here and that used by Shi et al. [2] are basically similar, i.e. to reduce the effect of residue stress and strain. The difference in the heat treatment, i.e. 24 h at 60°C by Shi et al. [2] and 20°C for 30 days in the present study, are not expected to introduce any significant variations in the properties of these solders [9]. The plots of both Shi et al. [2] and the present results show the decrease in time to failure with increasing strain rate and fall on the double-linear line with the transition strain rate of approx. 10⫺3 s⫺1. This transition strain rate corresponds to the transition strain rate (e˙ w∗ ), which separates two regimes of deformation: one is the matrix deformation with grain boundary sliding at low strain rates and the other is the matrix deformation without grain boundary sliding at high strain rates. The piecewise power laws obtained from data fitting are indicated in the following form: (a) At the strain rates higher than 10⫺3 s⫺1, tf ⫽ 45.15e˙ ⫺0.96
(2)
(b) At the strain rates lower than 10
⫺3
⫺1
s ,
tf ⫽ 380e˙ ⫺0.65
(3)
In the high strain rate regime, the results of Cutiongco et al. [9] and Guo et al. [10], which include the effect of loading mode (pull–pull) as compared to push–pull used in this study, are in good agreement with the present results (Fig. 8). At present, the effect of loading mode of LCF of eutectic Sn–Pb solder is still unclear. However, the difference between push–pull and pull–
Table 2 The low cycle fatigue testing conditions Materials
Strain range
Temperature
Waveform
Failure definition
63Sn/37Pb
2%⌬eT
25°C
Triangular
Separation
63Sn/37Pb
0.6–2%⌬eT
25°C
Saw-tooth
63Sn/37Pb
0.5–2%⌬eT
25°C
Saw-tooth
62Sn/37Pb
0.5–2%⌬eT
20°C
Triangular
Heat treatment
Annealed at 60°C for 24 h in a N2 atmosphere Drop-in-stress Heat treated for 2 h at ratio (smax/smin) 150°C and left in air for 6–10 days Young’s Heat treated for 2 h at modulus drop 150°C and left in air for 6–10 days 25% reduction Electrolytically of maximum polished and fully tensile load aged at room temperature for more than 30 days
Loading mode
Ref.
Symmetrical uniaxial push– pull Uniaxial pull– pull
[2]
Uniaxial pull– pull
[10]
Symmetrical uniaxial push– pull
Present work
[9]
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pull modes is expected to be more significant at low strain rates where time-dependent damage processes dominate. The agreement observed at high rates is, therefore, not surprising.
4. Conclusion The effect of strain rate on the isothermal LCF mechanisms of Sn–Pb eutectic (63Sn/37Pb) solder have been studied at a constant temperature of 20°C. The main conclusions obtained are summarized as follows: 1. The relationships between number of cycles to failure (Nf) and strain rate showed the S-shaped characteristics. The slopes in the low strain rate regime and the high strain rate regime were nearly identical. The effect of strain rate on fatigue life became less with increasing total strain range. Cavitation due to grain boundary sliding was the dominant failure mechanism in the low strain rate regime, while cavitation without grain boundary sliding was the dominant mechanism in the high strain rate regime. The transition strain rate was approx. 10⫺3–10⫺4 s⫺1. 2. An estimation of the upper bound strain rate (e˙ ∗w) for wedge-type fracture in LCF based on the assumption of a linear shear resistance for the grain boundary and a power law behavior for the matrix yielded a value lower than the experimental value by 2–3 orders of magnitude. Therefore, it seemed that the assumption of a linear shear resistance for the boundary may not be valid in the case of the colony boundary of eutectic Sn–Pb studied here. 3. The relationship between time to failure and strain rate for the present results was in good agreement with the reported results [2,9,10]. The time to failure decreased with increasing strain rate. The relationship could be expressed by a double-linear curve with the transition strain rate of approx. 10⫺3 s⫺1.
Acknowledgements The authors would like to thank T. Ori, Oki Electric Industry Co. Ltd for supplying solder materials used in this work. They also express sincere thanks to Dr S.L. Mannan for useful discussion.
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