Correlation Between Solder Joint Fatigue Life and ... - IEEE Xplore

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IEEE TRANSACTIONS ON COMPONENTS, PACKAGING AND MANUFACTURING TECHNOLOGY, VOL. 5, NO. 9, SEPTEMBER 2015

Correlation Between Solder Joint Fatigue Life and Accumulated Work in Isothermal Cycling Sa’d Hamasha, Awni Qasaimeh, Younis Jaradat, and Peter Borgesen

Abstract— The fatigue behavior of solder joints in realistic service applications is still not well understood. Service life prediction based on conducting accelerated tests and extrapolating test results therefore involves a high potential for error. Understanding both the evolution of solder joint properties and the damage accumulation has proved to be critical to reliability modeling. Damage accumulation in isothermal cycling is shown to scale with the accumulated inelastic work even in complex cycling scenarios, so that the life of a solder joint ends upon accumulation of a given amount of work. Individual ball grid array solder joints were cycled in shear fatigue experiments with different load amplitudes and strain rates. The effects of load amplitudes and strain rates on the work accumulation and fatigue life were systematically addressed. The correlation between different loading scenarios and the accumulated work to failure was also discussed. The results showed that the accumulated work until the development of a major crack is constant regardless of the load amplitude. After that the accumulated work to failure is lower for larger load amplitudes. For some reason, a larger fraction of the work appears to be dissipating as heat at lower load amplitude, but only during crack growth. On the other hand, the strain rate affects the fraction of the work going to heat even before the development of a major crack. Index Terms— Fatigue, reliability, solder, work accumulation.

I. I NTRODUCTION

T

HE extrapolation of accelerated test results to fatigue life in long term service is invariably complicated by our inability to directly verify predictions. There is, however, an almost general consensus that there is a direct correlation between stored energy and fatigue damage [1]. This has been shown to extend into the high cycle regime where it fits the empirical Basquin relation [1]–[3]. That is of interest in its own right, but when it comes to the fatigue of lead free solder joints the correlation may be even more important because it serves as the basis for an approach being developed to account

Manuscript received October 11, 2014; revised March 21, 2015 and June 15, 2015; accepted July 4, 2015. Date of publication August 6, 2015; date of current version September 18, 2015. This work was supported in part by the National Science Foundation under Grant DMR 1206474 and in part by the U.S. Department of Defense through the Strategic Environmental Research and Development Program. Recommended for publication by Associate Editor S. K. Sitaraman upon evaluation of reviewers’ comments. (Corresponding author: Sa’d Hamasha.) S. Hamasha, Y. Jaradat, and P. Borgesen are with the Department of Systems Science and Industrial Engineering, Binghamton University, Binghamton, NY 13902 USA (e-mail: [email protected]; yjarada1@binghamton. edu; [email protected]). A. Qasaimeh is with the Department of Manufacturing and Engineering Technology, Tennessee Tech University, Cookeville, TN 38505 USA (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TCPMT.2015.2453989

for the sometimes dramatic breakdown of current damage accumulation rules under realistic service conditions where cycling amplitudes vary on an ongoing basis [4]. Even if the amplitude is fixed, however, the question remains as to which part of the total work is stored where it can contribute to the evolution of damage. Thus, work dissipated as heat would not contribute to the nucleation, multiplication, and accumulation of dislocations, and the evolution of dislocation structures associated with damage. In addition, materials subject to an endurance limit will obviously disseminate an increasing fraction of the overall work without doing damage as amplitudes are reduced [2], [3]. Chang et al. [3] showed how accounting for this would allow for scaling of results for steel up to tens of millions of cycles. However, damage accumulating in regions away from the eventual failure location may, of course, also not be negligible. The evolution of damage in thermal cycling is further complicated by the effects of temperature variations and we have shown the damage per cycle not to vary with the total work accumulated in the cycle as commonly assumed [5]. Indications that the isothermal fatigue life of SnAgCu [6] solder joints may be determined by the accumulation of a total amount of inelastic work which does not vary with cycling amplitude might seem to offer a convenient means of extrapolating accelerated test results to high cycle fatigue conditions. However, like previously observed for SnPb [7], we shall show that more accurate measurements reveal a slow reduction in total work to failure as the amplitude is increased. This may have profound consequences for the extrapolations, as well as for predictions of damage accumulation under realistic service conditions [4], depending on whether the variation is associated with an endurance limit or with the fraction of work going to heat. Measurements near a potential endurance limit are difficult as hysteresis loops are almost immeasurably small there and primarily a result of nondamaging (anelastic) mechanisms. Measurements at higher amplitudes, however, may not easily reflect the actual value of a limit. Assuming an endurance hysteresis energy Wo and a fixed damage energy to failure W f , the total measured hysteresis energy per cycle W will lead to failure after N cycles, where [3] W f = N(W − W0 ) = Wtot − NW0

(1)

and Wtot is the total accumulated energy to failure. In that case Wtot will vary as a linear function of N. We note that this should be true whether we vary the cycling amplitude or the frequency (strain rate). Not surprisingly, as we shall see,

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HAMASHA et al.: CORRELATION BETWEEN SOLDER JOINT FATIGUE LIFE AND ACCUMULATED WORK IN ISOTHERMAL CYCLING

Fig. 1. Cross polarizer images of cross section of 30-mil SAC305 solder joints showing (a) beach-ball and (b) single-grain structures.

load controlled cycling with a lower strain rate leads to a greater W and smaller N. An endurance limit should thus cause the total inelastic work to failure to increase with decreasing amplitude and increasing strain rate. The question is how to distinguish this behavior from effects of variations in the fraction of W that goes to heat. It does not appear to be a priori predictable how this fraction will vary with strain and strain rate for a given metal, especially one with a significant Bauschinger effect [8]. The fraction of work going to heat has been seen to increase with strain rate for both single and polycrystalline Cu [9], and Hodowany et al. [10] and Rosakis et al. [11] found the same for α-titanium but not for an aluminum alloy. The fraction also increased with cycling amplitude in steel [12], [13]. To the extent that these trends apply to solder as well and dominate variations the total work should then increase with strain rate and amplitude. The amplitude dependence is the opposite of what is observed in this paper. A limited amount of work has been published on the behavior of individual SnAgCu solder joints in isothermal cycling, but almost all using unrealistically large samples almost certainly composed of a number of Sn grains with distributions of the secondary precipitates unlike those formed in the reflow of realistic Ball Grid Array (BGA) scale joints [14]–[16]. This paper focuses on 30-mil diameter BGA joints with a single Sn grain or a so-called beach-ball structure (Fig. 1). This paper focuses on room temperature cycling. Cycling at higher temperatures is complicated by a simultaneous coarsening of the secondary precipitates in the SnAgCu type alloys. The correlation between the damage rate and the work per cycle applies only to isothermal cycling. Failure in thermal cycling is controlled by global recrystallization followed by crack propagation along the new network of grain boundaries [17] and the damage rate appears to scale with the rate of work during the high temperature dwell alone [5]. In contrast, damage in isothermal cycling occurs by transgranular crack growth [18]–[22].

Fig. 2.

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Schematic of the shear fatigue fixture with a solder joint.

Fig. 3. Load–displacement loop for an SAC305 solder joint cycled with an amplitude of 500 gf.

II. M ATERIAL AND M ETHODS

is noticed. Consistent with this the displacement amplitude, effective stiffness and work per cycle levels off (below). The shear stress is concentrated in a region just above the pad surface [4]. We approximate the average shear stress there as the applied load divided by the pad area. The present test samples were prepared from 0.75-mm diameter solder spheres of the SAC305 alloy. These spheres were soldered onto 0.55-mm diameter copper pads on typical BGA component substrates. The soldering was done by printing a tacky flux through a stencil onto the substrate pads, placing the solder balls through apertures in a separate stencil and reflowing the component in a nitrogen ambient with less than 50-ppm oxygen using a Vitronics-Soltec 10-zone full convection oven. The reflow profile had a peak temperature of 245 °C and 45–60 s above liquidus. Fig. 3 shows an example of a load–displacement, or hysteresis, loop for a joint cycled with an amplitude of 500 gf. The inelastic work for each cycle was calculated from the area enclosed within the loop using numerical integration implemented by MATLAB. The initial slope of the load–displacement curve in each cycle provides an empirical measure of the effective stiffness of the joint in the plane of loading.

Individual ball grid array solder joints were isothermally cycled in shear fatigue using an instron micromechanical tester. Load and displacement data were continuously recorded, generating a hysteresis loop for each cycle. Fig. 2 shows a schematic of the shear fatigue experiment. The first few cycles lead to limited flattening of the solder joint in the contact area, after which no significant additional flattening

Monitoring the changes in the effective stiffness and work versus cycle number provides for an understanding of the solder joint behavior during isothermal cycling [4]. Kanchanomai and Mutoh [23] tested bulk dog-bone SnAg samples in tension–compression with fixed displacement

III. R ESULTS AND D ISCUSSION

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Fig. 4. Correlation between plastic strain and fatigue life of SAC305 solder joints.

Fig. 5. Inelastic work per cycle in isothermal cycling of an SAC305 solder joint [4], [24].

amplitudes and reported Coffin–Manson relation α

good

agreement

ε p N = Constant

with

Fig. 6.

Average work per cycle as a function of cycling stress amplitude.

Fig. 7. Characteristic life of SAC305 solders in isothermal cycling as a function of stress amplitude.

the (2)

when taking N as the number of cycles to 25% load drop, i.e., until the development of a major crack. Here, ε p is the plastic strain range and α is the so-called fatigue ductility exponent. Kanchanomai and Mutoh [23] found a value for α of about −0.95, i.e., an almost linear relationship. Our results for realistic BGA SAC305 joints also agree with (2), albeit with α = −0.71 (Fig. 4). Kanchanomai and Mutoh [23] did, however, report better agreement with a dependence on plastic strain energy density with separate dependencies on frequency (strain rate) and temperature. We agree with Kanchanomai and Mutoh [23] that a correlation with stored energy is more intuitive, and there is a growing consensus as to a general validity for metals [1]. Fig. 5 shows the typical behavior of inelastic work per cycle in isothermal cycling of an SAC305 solder joint with fixed load amplitude [4], [24]. The initial drop in work per cycle represents solder joint flattening, due to the contact between the cylindrical tip and the solder sphere, and possibly strain hardening. Then the rate of inelastic work stays constant (steady state) for the majority of the solder joint life without additional contact effect. At some late point of the fatigue life (80%–90%), the damage accumulation leads to significant crack growth and thus a significant increase in the work per cycle until failure.

The work per cycle during steady-state varies from one solder joint to another for the same cycling stress amplitude. This variability is primarily due to the random Sn grain orientations [4]. Therefore, a minimum of seven replicates were used to calculate the averages and reveal trends. Fig. 6 shows the average work per cycle in the steady-state region as a function of stress amplitude. As expected the work per cycle significantly varies with the stress amplitude; higher stress amplitudes depositing more work per cycle with a power of 6.23. Higher stress amplitudes also lead to more damage per cycle. As a result, the fatigue life (number of cycles to failure) strongly varies with the amplitude. Fig. 7 shows the characteristic life (N63 ) of SAC305 solder joints in isothermal cycling varying with the stress amplitude to a power of −6.5. Fig. 8 shows the average damage per cycle (1/N63 ) over the life as a function of average steady-state work per cycle for different stress amplitudes. We notice a strong direct correlation between the two [25]. Fig. 9 does, however, show the average accumulated work to failure for SAC305 solder joints to slightly and systematically vary with amplitude; the lower the amplitude, the higher the accumulated work. Still, the variation in the accumulated work is within a factor of 2 while the variation in fatigue life for the same range of amplitudes is about a factor of 35. More importantly, extrapolating the accumulated work to failure to very low amplitudes, say 0.1 MPa, leads to


Fig. 8. Correlation between the average damage per cycle and the average work per cycle.

Fig. 9. Average accumulated work until failure for SAC305 alloy as a function of load amplitude.

Fig. 10. Cumulative density function of accumulated work to failure of SAC305 solder joints cycled with single and varying loads.

a variation in the accumulated work at failure of less than a factor of 3, if the apparent linear relationship between the accumulated work and amplitude continues. Considering the much stronger variation in fatigue life suggested by the power correlation between life and amplitude this may not be a serious concern. However, if the variation in Fig. 9 is in fact a result of an endurance limit, rather than a systematic variation in the fraction of the overall work going to heat, a linear extrapolation would be extremely conservative. The work accumulation in isothermal cycling is seen to scale with the fatigue life even in complex cycling scenarios. Fig. 10 shows the cumulative density function of the

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Fig. 11. Average total work to failure versus characteristic life of SAC305 solder joints cycled with different stress amplitudes.

Fig. 12. Progression of the accumulated work until failure for SAC305 solder joints at different load amplitudes.

accumulated work to failure of SAC305 solder joints cycled with fixed and varying amplitudes. It is obvious that there is no significant variation in the accumulated work to failure between cycling with fixed loads and varying loads. Fig. 11 shows the work to failure as a function of the characteristic life N63 . The systematic deviation from a linear dependence (1) would seem to be an argument against an endurance limit being the dominant factor. Also, Fig. 12 shows the work accumulation over the course of the fatigue life for SAC305 solder joints cycled with different load amplitudes. The work accumulation is seen to progress at an almost constant rate, and scale with the fraction of life for the different load amplitudes, until a relatively late stage, 80%–90% of life. After that the work accumulates rapidly and with a systematic dependence on the load amplitude. Monitoring the effective stiffness level allows us to detect the crack initiation and propagation [25]. Fig. 13 shows the evolution of the effective stiffness for an SAC305 solder joint in isothermal cycling. The continuous drop in the effective stiffness is due to crack growth, but it is strongly enhanced by the resulting softening due to the increase in stress amplitude [25], [26]. This prevents the quantification of crack lengths from the variation in stiffness or associated range of displacement [25]. Somewhat arbitrarily, we define a major crack based on the change in effective stiffness as shown in Fig. 13. This point is indicated on each curve in Fig. 12.

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Fig. 13. Effective stiffness of an SAC305 solder joint in isothermal cycling.

Fig. 14. Accumulated work before and after developing a major crack as a function of load amplitude.

Fig. 14 shows the average of the accumulated work for a total of 40 joints before and after developing a major crack as a function of load amplitude. It is obvious that the accumulated work is almost independent of the load amplitude until a major crack has developed. Only after that does the accumulated work become more load dependent; the lower amplitudes requiring more accumulated work to failure. This is consistent with dye-and-pry measurements on BGA joints by Qasaimeh et al. [25]. Also, the results in [23] for bulk SnAg samples in tension–compression cycling agree with the accumulated work to develop a major crack slowly decreasing with increase in amplitude. In load controlled cycling, the true stress amplitude rapidly increases as the crack grows, so effects of an endurance limit should be decreasing there. This would not explain the much greater sensitivity to amplitude during the growth of a major crack. Effects of the work going to heat may increase with stress amplitude, but probably in the opposite direction [12], [13]. The almost linear relationship between the number of cycles to develop a major crack and the plastic work per cycle reported in [23] could suggest an almost constant accumulated strain to failure, whereas our results for realistic SAC305 joints do not. Fig. 15 shows the average accumulated plastic strain until failure together with the accumulated plastic strain before and after developing a major crack as functions of load amplitude. Comparing with the accumulated work until

Fig. 15. Accumulated plastic strain until failure and before and after developing a major crack as a function of load amplitude.

failure (Fig. 9), it is obvious that the accumulated plastic strain until failure significantly varies more with load amplitude; it varies within a factor of 6 while the variation in accumulated work for the same range of amplitudes is about a factor of 2. More importantly, the variation in the accumulated plastic strain until developing a major crack is about a factor of 3 while the accumulated work until onset of cracking is almost constant. In general, a major fraction of the accumulated work in isothermal cycling of a metal is dissipated as heat [27], [28]. After the development of a major crack the friction between cracked surfaces must cause more heat so that a larger fraction of work now goes to heat. We tentatively suggest that this fraction increases as we reduce the amplitude. Alternatively, the distribution of damage to the lattice elsewhere in a heavily deformed joint may of course vary with the load amplitude. This does not mean that there is no endurance limit. The trend in Fig. 15 could not be explained by an endurance limit, but the accuracy of the present measurements does not allow us to decide whether the apparent small decrease in the work to develop a major crack is in fact a result of such a limit. In fact, while variations in the fraction of the work that goes to heat before cracking may not be a priori predictable [8], the indication from studies of other metals suggests that it should increase with amplitude [12], [13]. However, if the decrease in the work required to develop a major crack is only due to an endurance limit, this would have to be on the order of 1 μJ for the present joints. Whatever its cause the variation with load amplitude is not unique to SAC305. Fig. 16 shows the average accumulated work to failure as a function of load amplitude for three SnAgCu alloys and eutectic SnPb. The accumulated work until failure is significantly lower for SnPb than for the SnAgCu alloys, but the general trend is the same for all these solder alloys. The amount of work per cycle also significantly varies with strain rate (frequency of cycling). Thus the fatigue life in load controlled cycling quite strongly varies with strain rate. Fig. 17 shows the fatigue life of SAC305 solder joints at a fixed load amplitude of 24 MPa for different strain rates. The curve reflects a variation with strain rate to a power of 0.13.


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Fig. 16. Accumulated work to failure for different solder joint alloys as a function of load amplitude.

Fig. 19. Average total work to failure versus characteristic life of SAC305 solder joints cycled with different strain rates.

Fig. 17. Characteristic life of SAC305 solders in isothermal cycling with fixed amplitude as a function of strain rate.

Fig. 20. Progression of the accumulated work to failure for SAC305 solder joints cycled with same load amplitude and different strain rates.

Fig. 18. Average accumulated work to failure for SAC305 solder joints as a function of strain rate.

Cycling with a lower strain rate creates more work in each cycle and thus leads to shorter fatigue life. Fig. 18 shows the average accumulated work to failure as a function of the strain rate for SAC305 solder joints cycled with fixed load amplitude of 24 MPa. It is obvious that the accumulated work to failure slightly increases with the strain rate. Fig. 19 shows the work to failure as a function of the characteristic life N63 . Unlike when the amplitude was varied, these results could be consistent with a linear dependence. However, assuming the variation is due to an endurance limit

Fig. 21. Accumulated work before and after developing a major crack as a function of strain rate.

the fit suggests a value of about 40 μJ, i.e., much greater than implied by the effect of amplitude unless the small variation in Fig. 14 includes a counteracting effect of variations in the fraction of work that goes to heat. The variation in Fig. 18 is more likely to be related to the fraction of the work going to heat. Measurements on single crystal Cu and other metals [9], [10], including bulk SnAg [23], all showed the fraction to increase with strain rate. The effect is quite limited for the present SAC305 joints. Unlike load amplitude, the strain rate affects the work accumulation through the entire solder joint life. Fig. 20 shows

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representative examples of the work accumulation as a function of the fraction of total life for SAC305 solder joints cycled with the same load amplitude and different strain rates. The joint cycled with the higher strain rate tends to require the accumulation of more work to reach a certain level of damage from the very beginning. Fig. 21 shows the average accumulated work in SAC305 solder joints before and after developing a major crack as a function of strain rate. The relative effect is the same as would be expected if it is associated with the fraction of the work going to heat. IV. C ONCLUSION Prediction of service life based on accelerated tests results can be misleading without a proper constitutive relation. Understanding the behavior of damage accumulation through the solder joint fatigue life is critical to reliability modeling. The damage accumulation has been shown to scale with work accumulation in isothermal cycling. The life of a solder joint in isothermal cycling thus appears to end upon accumulation of a given amount of work. However, the total work until complete failure of realistic SAC305 solder joints actually slightly decreases with increase in load amplitude and slightly increases slightly with increase in strain rate (to a power of 0.13). The latter is consistent with a limited variation in the fraction of the overall work that goes to heat. The total work to crack initiation is almost independent of load amplitude, whereas the accumulated work after that is stress dependent. We speculate that friction between crack surfaces causes additional heat so that a larger fraction of the work now goes to heat and that this fraction increases as we reduce the amplitude. As a practical approximation, we propose that accelerated test results can be extrapolated to cycling with a different amplitude according to N =c

ε0.13 Wc

where c is a constant for a given solder joint size and cycling configuration, ε is the strain rate, and Wc is the work per cycle. This paper did not account for the complex stress distribution throughout a joint. The fatigue life is actually expected to vary with the local distribution of work in the high strain region. However, ongoing work is showing the constitutive relations to vary with cycling to the extent that the dominant creep mechanism may change as well. Until this is resolved, finite element modeling efforts would be misleading. R EFERENCES [1] J. Warren and D. Y. Wei, “A microscopic stored energy approach to generalize fatigue life stress ratios,” Int. J. Fatigue, vol. 32, no. 11, pp. 1853–1861, 2010. [2] J. Wertz, C. Holycross, M.-H. H. Shen, O. Scott-Emuakpor, T. George, and C. Cross, “A comparison of constitutive equations for the energybased lifing method,” J. Eng. Mater. Technol., vol. 135, no. 3, p. 031008, 2013. [3] C. S. Chang, W. T. Pimbley, and H. D. Conway, “An analysis of metal fatigue based on hysteresis energy,” Experim. Mech., vol. 8, no. 3, pp. 133–137, 1968.

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Awni Qasaimeh, photograph and biography not available at the time of publication.

Sa’d Hamasha, photograph and biography not available at the time of publication.

Peter Borgesen, photograph and biography not available at the time of publication.

Younis Jaradat, photograph and biography not available at the time of publication.