Assessment of Solder Joint Fatigue Life Under ... - Springer Link

Journal of ELECTRONIC MATERIALS, Vol. 43, No. 12, 2014

DOI: 10.1007/s11664-014-3436-3 Ó 2014 The Minerals, Metals & Materials Society

Assessment of Solder Joint Fatigue Life Under Realistic Service Conditions SA’D HAMASHA,1,3 YOUNIS JARADAT,1 AWNI QASAIMEH,2 MAZIN OBAIDAT,1 and PETER BORGESEN1 1.—Department of Systems Science & Industrial Engineering, Binghamton University, P.O. Box 6000, Binghamton, NY 13902, USA. 2.—Department of Manufacturing and Engineering Technology, Tennessee Tech University, Cookeville, TN, USA. 3.—e-mail: [email protected]

The behavior of lead-free solder alloys under complex loading scenarios is still not well understood. Common damage accumulation rules fail to account for strong effects of variations in cycling amplitude, and random vibration test results cannot be interpreted in terms of performance under realistic service conditions. This is a result of the effects of cycling parameters on materials properties. These effects are not yet fully understood or quantitatively predictable, preventing modeling based on parameters such as strain, work, or entropy. Depending on the actual spectrum of amplitudes, Miner’s rule of linear damage accumulation has been shown to overestimate life by more than an order of magnitude, and greater errors are predicted for other combinations. Consequences may be particularly critical for so-called environmental stress screening. Damage accumulation has, however, been shown to scale with the inelastic work done, even if amplitudes vary. This and the observation of effects of loading history on subsequent work per cycle provide for a modified damage accumulation rule which allows for the prediction of life. Individual joints of four different Sn-Ag-Cu-based solder alloys (SAC305, SAC105, SAC-Ni, and SACXplus) were cycled in shear at room temperature, alternating between two different amplitudes while monitoring the evolution of the effective stiffness and work per cycle. This helped elucidate general trends and behaviors that are expected to occur in vibrations of microelectronics assemblies. Deviations from Miner’s rule varied systematically with the combination of amplitudes, the sequences of cycles, and the strain rates in each. The severity of deviations also varied systematically with Ag content in the solder, but major effects were observed for all the alloys. A systematic analysis was conducted to assess whether scenarios might exist in which the more fatigue-resistant high-Ag alloys would fail sooner than the lower-Ag ones. Key words: Solder, reliability, fatigue, damage accumulation

INTRODUCTION The long-term reliability of electronic products is often limited by the fatigue failure of one of the interconnects due to thermal and/or isothermal cycling. The most common approach to the assessment of fatigue life is based on conducting an accelerated (Received May 3, 2014; accepted September 20, 2014; published online October 9, 2014)

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test. In the absence of a model, this relies, at the very least, on the assumption that the assembly that performs better in test also performs better under service conditions, but that assumption is not necessarily true. It is quite common for acceleration factors for lead-free solder joints to vary with alloy, dimensions, pad finishes, and process parameters. In addition, the accelerated fatigue test is most commonly done by applying a constant amplitude in cycling until failure, whereas an assembly in real

Assessment of Solder Joint Fatigue Life Under Realistic Service Conditions

service is subjected to varying values of stress amplitudes and strain rates. Such an overall combination also cannot be counted on to be better represented by the spectrum of amplitudes in, for example, a random vibration test. Variations in stress amplitude and strain rate may in principle be accounted for by a model based on, for example, the accumulated work, but we shall show that this is not practical for solder. The assessment of service life based on extrapolations of accelerated fatigue test results may therefore be very misleading. The present work focuses on room-temperature cycling with no dwell at any load. The results are also expected to be relevant to cycling with a limited dwell. Cycling at higher temperatures and/or for very long times (high cycle fatigue) may be complicated by a simultaneous coarsening of the secondary precipitates in the SnAgCu-type alloys considered. To the extent that this is properly accounted for a forthcoming publication will offer support for the common assumption of a correlation between stored energy and fatigue damage,1–4 and work is ongoing to verify preliminary indications that the general outcome of the present work is also relevant to high cycle fatigue in vibration. The correlation between the damage rate and the work per cycle does, however, only apply for isothermal cycling. Failure in thermal cycling is controlled by large-scale recrystallization followed by crack propagation along the new network of grain boundaries,5 unlike damage in isothermal cycling which occurs by transgranular crack growth.6–10 Thermal cycling therefore leads to a completely different damage accumulation scenario11 for which the present results are not relevant. Effects of amplitude variations may in principle be accounted for through any model that relates damage accumulation to, for example, stress, strain, creep, work, or entropy. As we shall see, however, we can in fact not know the constitutive relationships to use to calculate either of these parameters under the conditions of interest. Alternatively, service life is commonly predicted based on damage accumulation rules such as Miner’s rule.12 Miner defined a term called the Cumulative Damage Index (CDI). The CDI is the summation of damage ratios during the fatigue cycling as in Eq. 1: X ni ; (1) CDI ¼ Ni where ni is the number of cycles at a particular amplitude i, and Ni is the fatigue life at amplitude i. According to Miner’s rule, the material will fail when the CDI equals 1. For example, cycling a component until 10% of its life is consumed with one value of amplitude, the component is expected to have 90% of life remaining with any other amplitude. Miner’s rule breaks down for SAC alloys particularly in combinations of different types of accelerated tests such as sequences of thermal cycling and vibration.13

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It also breaks down when just alternating between two amplitudes.14 A simple example was isothermal cycling of SAC305 solder joints with a high load amplitude until 60% of its life was consumed, followed by low amplitude cycling to failure. The remaining life was expected to be 40% based on Miner’s rule, but actually it was less than 4%.14 Figure 1 shows another example of the breakdown of Miner’s rule in varying amplitude cycling. Individual SAC305 solder joints were isothermally cycled, alternating between a mild amplitude of 16 MPa for 100 cycles and a harsh amplitude of 24 MPa for 5 cycles. This combination of amplitudes was repeated five times, and then the joints were cycled with an amplitude of 16 MPa to failure. The remaining life at the mild load was expected to be 77% based on Miner’s rule, but the actual remaining lives were found to scatter between 7% and 38%. As we shall see, the deviation from Miner’s rule may become much greater for larger differences between the amplitudes. The breakdown of current damage accumulation rules is an obvious concern with respect to quantitative predictions of life.15 Varying amplitude cycling of SAC305 solder joints under combinations of two different amplitudes showed significant life reduction compared with predictions based on fixed amplitude data.16 The breakdown is also a concern when it comes to comparisons. A preliminary study showed a similar trend for SnAgCu alloys with different Ag contents.16 However, as we shall see below, there is an overall tendency for low-Ag alloys to be less sensitive to variations in amplitude. The question therefore arises whether there are some realistic service conditions under which these may survive longer than SAC305. In the following, we will show the effect of variable loading on different types of lead-free solder joints. Furthermore, we will present the concept of hysteresis energy amplification in variable loading and explain how it could be used to modify Miner’s rule to allow accurate life prediction under real service conditions without the need to calculate the work. The modified life prediction rule is used to

Fig. 1. The actual remaining life under 16 MPa cyclic loading after consumption of 23% of life under varying amplitudes according to Miner’s rule.

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Hamasha, Jaradat, Qasaimeh, Obaidat, and Borgesen

generalize results for the different alloys to determine the degree of deviation from Miner’s rule and the sensitivity to varying amplitude cycling for each alloy. A comparison between the lead-free alloys is performed in terms of performance under varying amplitude fatigue. MATERIALS AND METHODS The properties of a SnAgCu type solder joint are governed by the microstructure, i.e. the orientations of the Sn grains and the precipitate distributions as well as evolving defects.17–21 Realistic size solder joints are usually formed in a single solidification event after substantial undercooling, leading to a cyclically twinned structure with a number of twin boundaries22 but no conventional grain boundaries. This and the associated precipitate distributions are very different from what is found in ‘bulk’ samples, making the testing of realistic solder joints important. A requirement for testing of individual joints separately limits the applicable test methods, but this requirement is important because of the strong variations in properties from joint to joint. Some of the general trends could also be elucidated by comparisons of averages over many joints, but a forthcoming publication will show how the magnitudes of some effects tend to be reduced by such averaging. Isothermal shear fatigue experiments were conducted on individual lead-free solder joints at room temperature. The solder joints were cycled using an Instron micromechanical tester. The Instron tester records the load and displacement data continuously, which provides the hysteresis loop for each cycle. Based on this, the inelastic work and effective stiffness for each cycle were calculated. The Instron offers displacement control through the use of a preloaded ball screw drive system equipped with both a rotary encoder and a 20-nm-resolution linear glass-scale encoder. Displacements by the linear encoder do of course include load cell, and load frame deflections, as well as test specimen deflection. The electromechanical (non-hydraulic) drive system has a stiffness (without specimen) between 600 gf/lm and 2000 gf/lm depending on the crosshead position. The fixturing does, however, lead to a reduction in this. The overall machine stiffness was measured to exceed that of our solder joints by a factor of about 3. This is by no means negligible, but we have chosen not to correct for this. The effective stiffness of the joint in question at any given time is simply calculated from the nominal stress (load divided by the area of the solder pad surface) and is, as mentioned below, only used for qualitative comparisons. The values for work per cycle, however, should not depend on the machine stiffness and are believed to be accurate. Figure 2 shows a schematic of the top and side views of the shear fatigue fixture with a solder joint. The first few cycles lead to limited flattening of the solder joint in the contact area,

Fig. 2. Top and side views of the shear fatigue fixture with solder sphere.

after which no significant additional flattening is noticed and the shear stress is concentrated in a region just above the pad surface.23 The typical test samples were 30-mil-diameter solder spheres of four different alloys. These spheres were soldered onto 22-mil-diameter copper pads on typical ball grid array (BGA) component substrates and tested one at a time. Table I shows the compositions. The attachment 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. Figure 3 shows examples of load–displacement loops, or hysteresis loops, for SAC305 joints cycled with two amplitudes (12 MPa and 20 MPa). The inelastic work in each cycle was calculated from the area enclosed within the load–displacement loops. The initial slope of the curve as the load increases from zero provides an empirical measure of the effective stiffness of the joint in the plane of loading. Elastic deformation of the tester was, as said, not negligible, but major systematic differences were still observed between the effective stiffnesses of the different alloys, and the stiffness of a given joint was seen to vary significantly during cycling (below). SOLDER BEHAVIOR IN CYCLIC LOADING As said, the need to test individual solder joints separately limits the applicable test methods significantly. There is such a need because the individual parameters are found to vary differently from joint to joint. Thus, as shown in a forthcoming publication, there is no correlation between, for example, the variations in effective stiffness and work per cycle, or the work and the amplification of the work (see below), due to amplitude variations from joint to joint. However, there is a clear correlation between stiffness and work for a given joint. Our shear fatigue experiment involves testing with in situ monitoring of one joint at a time, but the technique is far from perfect. Notably, the load is applied at the height of the largest cross-section of


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Table I. Compositions of the lead-free alloys Alloy SAC305 SAC105 SAC-Ni SACX-plus

Composition 3.0%Ag, 0.5%Cu 1.0%Ag, 0.5%Cu 1.2%Ag, 0.5%Cu, 0.05%Ni 0.3%Ag, 0.7%Cu, 0.05%Ni, 0.08%Bi

Fig. 4. The effective stiffness in SAC305 alloy under 16 MPa load control cycling.

Fig. 3. Load–displacement loops for SAC305 joints cycled with two different amplitudes (12 MPa and 20 MPa).

each joint (Fig. 2), and calculations of the resulting stress distributions would require knowledge of the constitutive relations that we cannot have, at least not after some cycling (see below). Stress amplitudes in the following are therefore nominal values and only included for qualitative reference. The values for work, however, are believed to be accurate and are the ones actually used in calculations. The behavior of our lead-free solder joints under cyclic loading can be understood by monitoring the changes in the effective stiffness and the inelastic work. Figure 4 shows the typical behavior of the effective stiffness in cycling with a fixed load amplitude. The initial few cycles lead to an increase in the effective stiffness. This is due to the combination of initial flattening and hardening of the solder joint.16 Thereafter, the level of effective stiffness stays constant through most of the solder joint life. Eventually, the accumulated damage then causes crack initiation and growth, and finally failure. The period of crack growth can be seen by the significant drop in the effective stiffness, although as we shall see we cannot simply infer crack sizes from the load drop. As is typical in load controlled cycling, the crack growth stage is limited, taking up the last 10–20% of the overall life. The effective stiffness values vary significantly from one solder joint to another. Such variability is common for SnAgCu solder joints and can be ascribed to variations in the orientations of the strongly anisotropic Sn grains relative to the loading direction24 and, to a lesser extent, to variations in the secondary precipitate distributions. Overall,

Fig. 5. The effective stiffness of the lead-free alloys as a function of the stress amplitude.

several replicates were therefore required to reveal systematic trends. Figure 5 shows the average effective stiffness during the steady state before crack initiation as a function of cycling amplitude for the different alloys. The initial hardening tends to occur faster for higher loading amplitudes but the steady state effective stiffness ends up lower. Work is ongoing to understand the latter effect, but the trend is the same for a given solder joint. Figure 6 shows the effective stiffness as a function of the cycle number for a particular SAC305 joint when the amplitude was varied. This joint was cycled with an amplitude of 16 MPa for 100 cycles and then with 24 MPa for 5 cycles. This sequence was repeated six times. The first thing we notice is that an increase in amplitude led to an immediate reduction in effective stiffness, in agreement with the trend in Fig. 4. More importantly, when returning to the low amplitude (16 MPa), the solder is seen to harden again but the effective stiffness level does not recover to the original level. Repeated returns to the higher amplitude are seen to further reduce the stiffness. The permanent effect of excursions to a higher amplitude is important because of the consequences for the accumulation of inelastic work.

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Fig. 6. The effective stiffness of SAC305 alloy in varying amplitudes cycling.

Fig. 7. Correlation between work per cycle and effective stiffness for a single SAC305 solder joint under varying amplitude loading.

The effective stiffness as measured is determined by the combination of not only the machine stiffness but also the elastic modulus of the solder, and the strain rate-dependent anelastic as well as the inelastic deformation of the solder during loading. It is therefore not surprising that, as mentioned above, a forthcoming publication will show that there is no strong correlation between the major joint-to-joint variations of stiffness and work per cycle, variations which we ascribe primarily to the Sn grain orientations. However, for a given solder joint where the orientation is fixed, they seem to vary together (Fig. 7). The effective stiffness variations shown in Fig. 6 therefore appear to reflect general changes in the primary creep properties and thus the work per cycle. These changes have direct consequences for the damage accumulation. Figure 8 shows the evolution of the inelastic work per cycle for a given joint when the amplitude is fixed. Corresponding to the effective stiffness, the initial drop is due to the combination of strain hardening and solders joint flattening. Thereafter, the stiffness and thus the creep properties and the work per cycle stay constant for the majority of the solder joint life. Finally, the work increases as the


effective stiffness is reduced by crack growth during the last 10–20% of the life. The work per cycle does of course vary with amplitude. Figure 9 shows the work when alternating the amplitude between 16 MPa for 100 cycles and 24 MPa for 5 cycles, repeating this sequence five times. The figure does not actually show the much higher work per cycle for the 24 MPa amplitude. However, it is clear that the reduced stiffness in 16 MPa cycling after exposure to the 24 MPa cycles corresponds to a jump, or ‘‘amplification’’, in the work level in the low amplitude cycling. Immediately after switching back to 16 MPa there is a large amplification relative to the level established just before the 24 MPa cycles. This then decreases to reach a steady state level within about 10 cycles, but the steady state work per cycle remains higher and is further amplified every time we change the amplitude. There is no corresponding effect of the mild cycles on the work in subsequent higher amplitude cycling, so the overall effect of varying the amplitude is faster accumulation of work afterwards. This explains the break-down of Miner’s rule. Work is ongoing to try to understand the effects of amplitude variations on the deformation properties, but until we can predict them quantitatively the fact that we know that the damage rate scales with the work per cycle does not allow us to predict directly the effects on the fatigue life. This problem may, however, be circumvented by a simple modification to Miner’s rule. DAMAGE ACCUMULATION RULE A number of damage accumulation rules predict life under varying cycling conditions based on measured or predicted values of life for each separate condition. Miner’s rule requires that the important material properties are the same after consumption of a given fraction of the total life, no matter what the loading history.12,23 This assumption is clearly not valid for the lead-free solders under variable loading, which is why the rule breaks down. In general, linear damage accumulation rules break down for one or both of two kinds of reasons. The first reason is stress dependency. In a stress-dependent scenario, the accumulated damage after the consumption of a specified fraction of fatigue life is different for different stress amplitudes. In a stress-independent scenario, they are not.25 The second reason is damage interaction where the course of accumulating damage at a specified stress amplitude can be permanently changed by first applying other amplitudes.25 Miner’s rule is a stress-independent and interaction-free rule. A forthcoming publication will show that the damage accumulation during shear fatigue testing of realistic SAC305 joints may be considered stress independent until a major crack has developed. After that a stress dependence is tentatively


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Fig. 8. The inelastic work per cycle until failure of the SAC305 alloy as a function of number of cycles.

Fig. 9. The inelastic work in a SAC305 joint in varying amplitude cycling at 16 MPa and 24 MPa.

ascribed to friction between opposing crack surfaces, an effect that may be unique to the experiment. Even if we focus on the stress-independent part of the life, Miner’s rule is incapable of predicting this. The reason for this is that damage accumulation in SnAgCu is interactive. Specifically, interruption of cycling at a given stress amplitude with a few cycles of higher stress amplitude seems to lead to permanent changes in the deformation properties, as reflected in a permanent drop in the effective stiffness of the solder joint. This also leads to amplification of the damage accumulation in subsequent low-stress amplitude cycling. In general, interaction effects can lead to shorter or longer fatigue life of a material than predicted by Miner’s rule. Most of the damage accumulation rules that have been proposed for interactive cases predict a shorter fatigue life than Miner’s rule and thus lead to heavier design structures.25 Most of these rules lack a clear physical mechanism to identify useful applications and require too many engineering experiments for application.26 However, these rules anyway do not work for solder joints. Some of the basic assumptions of these rules are violated by the solder joints’ behavior in varying

amplitude cycling. Shanley’s theory does, for example, assume that the interaction effect is a result of the damage done in the first cycle,25,27 but in the case of solder joints the interaction is repeated every time we change the amplitude. The Corten–Dolan theory is a famous and widely used theory for interactive cases.28 It assumes that damage accumulation is nonlinear and can be expressed in terms of the number of cycles in a powerlaw equation,29 and that the highest stress has an effect on damage accumulation at the lower stresses in varying amplitude cycling.30 At a first glance, this might seem applicable to the present case. The damage accumulation according to the Corten– Dolan model is expressed by28: X ni ri d ¼ 1; (2) N1 r1 i where N1 is the fatigue life at the highest stress r1, ni is the number of cycles at stress ri, and d is the Corten–Dolan exponent which is a material constant. However, this model has been found to provide estimates of fatigue life with large errors for other materials.28 Recent studies showed that the Corten–Dalan exponent is not actually a material constant but also depends on the load spectrum.28 Still, even that would not properly account for the increasing damage rate with each return to the higher amplitude for solder. Other experimentally based interaction theories, such as the Freudenthal–Heller theory,31 showed no practical application of life prediction of solder joints in varying amplitude cycling. The concept of work amplification together with the knowledge that failure occurs after the accumulation of a given amount of work led us to a modification of Miner’s rule for the combination of two alternating amplitudes11,16,32: 1¼

s X i¼0

f ðiÞ

nmi nhi þ ; Nm Nh

(3)

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Fig. 10. The amplification factor, f(i), as a function of the number ‘i’ of interruptions with a set of high amplitude cycles.

where nmi is the number of cycles at low amplitude, Nmi is the life at low amplitude, nhi is the number of cycles at high amplitude, and Nh is the life at high amplitude. The amplification factor f(i) is the hysteresis energy in the low amplitude cycles after exposure to ‘i’ sets of nhi high amplitude cycles divided by the hysteresis energy in the low amplitude cycles just before exposure to the first high amplitude. Figure 10 shows the amplification factor as a function of the number of sets of high amplitude cycles for cycling of a SAC105 joint in alternating sets of 50 cycles with an amplitude of 16 MPa and 2 cycles with an amplitude of 24 MPa. In the case of SnAgCu alloys, the amplification factors invariably tend to follow an approximately straight line,32 f(i) = ai + b. The original modified Miner’s rule ignored the higher amplification in the first few cycles at the lower amplitude immediately after switching from the higher amplitude, and assumed that the work level in each of the lower amplitude cycles stays constant. This assumption is, however, not a very good approximation in cases of cycling with only a few cycles in each set of lower amplitude cycles; in particular, not when the amplitude varies in every cycle as in random vibration. Figure 11 shows the work amplification at lower amplitude before and after interruption with two cycles of higher amplitude. The energy amplification after the interruption can be divided into initial amplification and steady-state amplification as noted in Fig. 11. The initial amplification is significantly higher than the steady-state amplification and it cannot be ignored if we are looking for accurate life prediction. Figure 12 shows the energy amplification factor for the first 5, 10, and 15 cycles of each low amplitude sequence together with the energy amplification at steady state as a function of the number of interruptions with high amplitudes. It is obvious that the slope of amplification in all cases is almost the same. The only difference is the offset in the linear equation. This offset is equal to 1 in the steady-state amplification.


Fig. 11. Inelastic work per cycle in SAC105 solder joint before and after interruption with higher amplitude.

Fig. 12. Energy amplification factor in SAC105 for the first 5, 10, and 15 cycles of each low amplitude sequence and the steady state as a function of the number of interruptions with a set of 2 high amplitude cycles.

Dividing the amplification factor into two states, a refinement of the modified Miner’s rule is achieved as: s X nin ðnmi nin Þ nhi f ðiÞin þ f ðiÞst þ (4) 1¼ Nm Nm Nh i¼0 with f ðiÞin ¼ ai þ bin

(5)

f ðiÞst ¼ ai þ 1;

(6)

and

where f(i)in is the amplification function in the initial state, f(i)st is the amplification function in the steady state, a is the slope of amplification, bin is the amplification constant in the initial state, nin is the number of cycles in the initial state, nmi is the number of cycles at low amplitude, Nmi is the life at low amplitude, nhi is the number of cycles at high amplitude, Nh is the life at high amplitude, and i is the number of intervals. The generalization to account separately for


each of the first few low amplitude cycles is obvious. We note, however, that switching back to a high amplitude after only a few low amplitude cycles every time will usually lead the high amplitude cycles to completely dominate the overall life, in spite of the amplification of damage in the low amplitude cycles. In that case, the breakdown of Miner’s rule will not have practical consequences. The slope of the amplification factor varies with alloy, high and low amplitudes, and the number of cycles in each set. Variations from one joint to another are also substantial. A higher value of the high amplitude causes a steeper slope of amplification for the SAC305 alloy.33 In addition, the slope of amplification in SAC305 increases with the number of high amplitude cycles in each set, but it soon levels off.16 This trend was observed for each of the 4 different alloys but with different degrees of sensitivity to the high amplitude values and number of cycles in each high amplitude set. The slope of the amplification factor also increases as the value of the low amplitude decreases if the high amplitude is constant. In general, the slope of the amplification thus increases with the difference between the low and high amplitudes. The number of mild cycles in each set, on the other hand, has no significant effect on the slope of the amplification. In the next section, we shall compare the four lead-free alloys, SAC305, SAC105, SAC-Ni, and SACX-Plus, in terms of performance under variable cyclic loading. Vibration The modified Miner’s rule can be applied to vibration and cyclic bending of assemblies even though we cannot measure the energy per cycle in such a test. Instead, we can measure the single amplitude life at harsh and mild loads, Nhi and Nmi, and if we can indeed assume a straight line we then only need the life for one combination of mild and harsh loads to solve Eq. 3 for the unknown a. In cases where the amplification factor cannot be approximated by a straight line, or when we need to use Eq. 4, we will need to test a few more combinations. Once we know f(i), we can calculate the life for any other combination of the loads. Importantly, the variations in amplification factors with the amplitude spectrum do show that a typical accelerated random vibration test does not offer a proper impression of what to expect in longterm service. A much better impression may be gathered from a forthcoming generalization of the modified Miner’s rule together with carefully selected combinations of vibration tests. LEAD-FREE SOLDER PERFORMANCES UNDER VARYING AMPLITUDES As discussed in the previous section, the life of a lead-free alloy in varied amplitude cycling can be

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Fig. 13. The inelastic work per cycle for SAC-Ni joint in alternating loading sequences of 50 cycles at 12 MPa and 7 cycles at 24 MPa.

predicted from the inelastic work amplification at low amplitude and the life in fixed amplitude cycling at both low and high amplitudes. A systematic study has been conducted on the different lead-free solder alloys in varying amplitude cycling. An ongoing effort is addressing the statistics of failure, showing the independent variations of the work and the amplification factors to lead to enhanced scatter of life under realistic service conditions where the amplitude varies. In the following, however, we limit ourselves to averages. For each solder alloy, 12–15 different combinations of loading scenarios were tested with five replicates for each combination. The average slopes of amplification for each combination were calculated. Figure 13 shows an example where an individual SAC-Ni solder joint was isothermally cycled in five repeated sequences of 50 cycles at 12 MPa and 7 cycles at 24 MPa. The amplification in the inelastic work per cycle is obvious. Figure 14 shows the average slope of amplification for SAC305 solder as a function of the number of high amplitude cycles in each set for three different combinations of loads. The low amplitude for these combinations was fixed at 16 MPa, but the high amplitudes were 20 MPa, 24 MPa, and 28 MPa, respectively. The slope of amplification is seen to increase with increasing number of high amplitude cycles, but it levels off after a few of these cycles. Also, a larger value of the high amplitude leads to larger values for the slope of amplification for any given number of high amplitude cycles, i.e. the whole curve shifts up. In addition, for the higher values of the high amplitude fewer cycles are required for the slope to level off. The other solder alloys show the same trend as SAC305 but with different degrees of sensitivity to the high amplitude and number of high amplitude cycles. We found that the lower silver alloys such as SAC105 show less amplification than SAC305. Figure 15 shows the average slope of amplification as a function of the number of high amplitude cycles for SAC105 with a low amplitude of 12 MPa and a high amplitude of 16 MPa, 20 MPa, and 24 MPa, respectively. It is obvious that the energy amplification for SAC105 is less than the amplification for

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Fig. 14. The average slope of amplification as a function of the number of high amplitude cycles in SAC305 solder for three combinations of amplitudes.

Fig. 15. The average slope of amplification as a function of high amplitude cycles in SAC105 solder with low amplitude of 12 MPa and high amplitude of 16 MPa, 20 MPa, and 24 MPa.

SAC305 for any combination with the same difference between the low amplitude and the high amplitude. So, the high silver alloy is more sensitive to varying amplitude cycling. On the other hand, it also has a greater fatigue life in single amplitude cycling. Figure 16 shows the fatigue life of SAC305, SAC105, SACX-Plus, and SAC-Ni in single amplitude cycling as a function of nominal stress. SAC305, with 3%Ag, is the most fatigue-resistant alloy, while SACX-Plus, with 0.3%Ag, is the least fatigue-resistant. There is no significant difference between SAC-Ni, with 1.2%Ag, and SAC105, with 1%Ag, in single amplitude cycling. Although the differences were smaller, the same ranking applied when compared for the same displacement amplitude, as opposed to load amplitude, so it can be considered general. This raises the question of whether varying amplitude conditions exist under which the lower Ag alloys may survive longer. Realistic service conditions may vary greatly for different samples of a given product. Reliability assessments and


Fig. 16. Characteristic life of lead-free solders as a function of nominal stress amplitude in single amplitude cycling.

warranties therefore commonly focus (or should focus) on the worst case scenario. Possible amplitudes obviously depend on the specific product and its intended uses. For purposes of illustration, we consider specifically a somewhat artificial case where our product is subjected to a particular loading history after which, according to Miner’s rule, the remaining life should be 90% of the original. Environmental stress screening (ESS) does, for example, rely on the assumption that the damage induced in ‘‘burn-in’’ reduces the life of the defect free product in subsequent service by no more than 10%.34 This requires an estimate of the remaining life. Limiting ourselves to isothermal cycling with varying amplitude, we define the ‘worst case scenario’ as the loading history for which the remaining life predicted by Miner’s rule is 90%, while the actual remaining life with a fixed amplitude is the lowest. For now, we furthermore limit ourselves to ‘‘burnin’’ using combinations of only two amplitudes. Work is ongoing to assess whether combinations of more than two amplitudes could be worse. Thus, we assume that we have cycled individual solder joints with two different amplitudes to consume 10% of their life according to Miner’s rule. Then, the actual remaining life is assumed to be consumed in fixed amplitude cycling. This remaining life is calculated using the modified Miner’s rule and experimentally measured amplification factors. As described above, if all other parameters are fixed, a lower mild amplitude will always lead to a greater deviation from predictions based on Miner’s rule, as long as the number of low amplitudes in each set is large enough to reach steady state. Keeping the mild amplitude fixed, we then aim to identify the ‘worst’ combination of the other parameters. We argue that the high amplitude parameters in this combination are almost independent of the mild amplitude chosen. A greater high amplitude always gives a stronger slope of the amplification factor, but it also creates more damage in each high amplitude cycle, and


thus only allows for fewer excursions to the high amplitude before we have consumed 10% of life (according to Miner’s rule). The worst case scenario for each alloy is thus defined by a trade-off between these factors. The low amplitude was kept constant with a fixed number of cycles while we changed the high amplitude, the number of high amplitude cycles, and the number of repetitions to consume 10% of life based on Miner’s rule. Table II shows the worst cases for SAC305 solder. The low amplitude cycling was kept as sets of 10 cycles with an amplitude of 16 MPa. Each column represents the worst combination of high amplitude and number of cycles. For example, the first row shows that applying 10 cycles at 16 MPa and 12 cycles at 18 MPa and repeating this 9 times should consume 10% of the solder life, according to Miner. The remaining life should thus be 90%, but actually the remaining life is 52.3%. This is the worst combination of 16 MPa and 18 MPa. The worst combination of 16 MPa and 20 MPa would involve only 4 cycles at 20 MPa in each set but 12 repeats of the 16–20 MPa combination. The overall worst combination with 16 MPa considered was 10 cycles at 16 MPa followed by 3 cycles at 24 MPa, repeated 8 times. In this case, the remaining life was 22.6%, as opposed to the 90% predicted by Miner’s rule. The cases shown in Table II were calculated based on measured amplification factors. There are worse cases that we have not measured, but we can predict them. Based on the correlation between the low amplitude value and work amplification,16 we can also extrapolate the results to lower amplitudes. Thus, extrapolating the SAC305 results from a low amplitude value of 16 MPa to 12 MPa, we found the worst case to be 10 cycles at 12 MPa followed by 3 cycles at 24 MPa, repeated 9 times. In this case, the remaining life would be 14.3% as opposed to the 90% predicted by Miner’s rule. The SAC105 alloy also shows significant deviations from Miner’s rule, but not as severe as SAC305. Table III shows the worst combinations of 10 cycles with an amplitude of 12 MPa with different higher amplitudes and cycle numbers measured for SAC105. The worst case scenario involved 10

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cycles at 12 MPa followed by 2 cycles at 18 MPa, repeated 16 times. In this case, the remaining life was 41.3%, as opposed to the 90% predicted by Miner’s rule. Table IV shows the worst combinations of 10 cycles with an amplitude of 12 MPa with different higher amplitudes and cycle numbers measured for SAC-Ni solder. The worst case scenario involved 10 cycles at 12 MPa and 1 cycle at 24 MPa, repeated 9 times. In this case, the remaining life was 40.3%, as opposed to the 90% predicted by Miner’s rule. The SAC-Ni and SAC105 thus show almost the same degree of deviation from Miner’s rule, 40.3% and 41.3% remaining life, respectively, but for slightly different sets of high amplitude cycles. The SAC-Ni showed slightly more sensitivity to the high amplitude value than SAC105 did. SACX-Plus was the weakest alloy in terms of fatigue resistance under single amplitude cycling and also shows significant sensitivity to variations in cycling amplitude. Table V shows the worst combinations tested for the SACX-Plus solder. The worst case scenario for SACX-Plus involved 10 cycles at 12 MPa followed by 1 harsh cycle at 24 MPa, repeated 7 times. In this case, the remaining life was 35%, as opposed to the 90% predicted by Miner’s rule. The SACX-Plus solder is thus more sensitive to variable loading than SAC105 and SAC-Ni, but not as sensitive as SAC305. Table VI shows a comparison of the worst case scenarios for the different solder alloys when the mild cycling is fixed as sets of 10 cycles with an amplitude of 12 MPa. The SAC305 is the most sensitive to varying amplitude cycling with a predicted remaining life of only 14.3%. However, it had the highest life in fixed amplitude cycling, so the actual remaining life at 12 MPa is still greater than for the others (4520 cycles). SACX-Plus is the second most sensitive alloy and has the lowest remaining life (920 cycles). SAC105 has a slightly longer remaining life at 12 MPa than SAC-Ni, 1870 cycles comparing to 1530 cycles. We did, however, set out to assess whether a loading history might exist for which the overall life of one of the lower-Ag alloys might end up longer than that of SAC305. Off hand, this would seem to

Table II. Worst combinations with sets of 10 cycles at 16 MPa for the SAC305 alloy High amplitude (MPa) 18 20 22 24 26 28 30

Cycles at high amplitude

Cycles at low amplitude

No. of repetitions

Miner prediction %

Modified Miner %

12 4 3 3 2 2 1

10 10 10 10 10 10 10

9 12 10 8 6 5 5

90 89.9 89.5 89.7 89.4 90.2 89.2

52.3 34 24 22.6 25.3 26 31.1

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Table III. Worst combinations with sets of 10 cycles at 12 MPa for the SAC105 alloy High amplitude (MPa) 16 18 20 22 24



No. of repetitions

Miner prediction %

Modified Miner %

6 2 2 1 1

10 10 10 10 10

11 16 10 12 9

90.4 90 90.2 90.3 89.8

42.1 41.3 42.4 48.6 50.9

Table IV. Worst combinations with sets of 10 cycles at 12 MPa for the SAC-Ni alloy High amplitude (MPa) 16 18 20 22 24



No. of repetitions

Miner prediction %

Modified Miner %

3 11 8 1 1

10 10 10 10 10

19 4 3 12 9

89.8 90.2 90.2 90.2 89.9

43.9 44.9 48.4 43.3 40.3

Table V. Worst combinations with sets of 10 cycles at 12 MPa for the SACX-Plus alloy High amplitude (MPa) 16 18 20 22 24



No. of repetitions

Miner prediction %

Modified Miner %

11 2 2 2 1

10 10 10 10 10

5 9 9 6 7

90.4 90.2 89.4 89.3 89.2

51.4 49 35 35.1 36.6

Table VI. Worst case scenarios of lead-free solders

Low amplitude/no. of cycles High amplitude/no. of cycles No. of repetitions Miner remaining life % Modified Miner remaining life % Modified Miner remaining life (cycles)

SAC105

SAC-Ni

SACX-Plus

SAC305

12 MPa/10c 18 MPa/2c 16 90% 41.3% 1870

12 MPa/10c 24 MPa/1c 9 90% 40.3% 1530

12 MPa/10c 20 MPa/2c 9 89.4% 35% 920

12 MPa/10c 24 MPa/3c 9 90.6% 14.3% 4520

Table VII. Preconditioning lead-free alloy with varying amplitude cycling

Mild load/no. of cycles Harsh load/no. of cycles No. of repetitions Remaining life at 12 MPa (cycles)

SAC105

SAC-Ni

SACX-Plus

SAC305

12 MPa/10c 24 MPa/1c 9 1930

12 MPa/10c 24 MPa/1c 9 1530

12 MPa/10c 24 MPa/1c 9 780

12 MPa/10c 24 MPa/1c 9 8860

be most likely to happen for the loading history that had the worst effect on SAC305, i.e. 10 cycles of 12 MPa followed by 3 cycles of 24 MPa, repeated 9

times. This left a total of 4520 cycles at 12 MPa (Table VI) for SAC305. However, even though the amplification factors were considerably lower for the


other alloys, this preconditioning by itself would do too much damage to those. Other combinations were therefore also considered. Table VII does, for example, show the results of pre-conditioning with sets of 10 cycles at 12 MPa followed by only 1 cycle at 24 MPa, repeated 9 times. For this and all the other possible combinations tested, the SAC305 still had the longest total life, and the SACX-Plus the shortest. In the majority of cases, the fatigue resistance of the SAC105 was larger than that of the SAC-Ni but in some cases it was not. All varying amplitude cycling experiments were done with a specific constant strain rate. Preliminary results show that the strain rate has a significant effect on varying amplitude cycling, especially as far as the energy amplification is concerned. Work is ongoing to quantify the effects of strain rate. In addition, we only considered combinations of two amplitudes. Work is also ongoing to assess the behavior of lead-free alloys under more amplitudes. Finally, additional alloys including Sn–Pb and SAC405 are also being tested in varying amplitude cycling. CONCLUSION The rate of damage in SnAgCu-based solder joints in isothermal cycling has been shown to scale with the work per cycle, but variations in cycling amplitude may lead to significant, permanent changes in the rigidity, and constitutive relationships are not currently available to account for this. Ignoring it may lead to overestimates of the remaining life in service after exposure to a few high stress events by orders of magnitude. Moreover, lower-Ag alloys which tend to be less fatigue-resistant are also less sensitive to variations in amplitude, raising the question as to whether they may in fact be superior under some practical conditions. The present trends were elucidated in shear fatigue testing of individual solder joints at room temperature, but in a general sense they are expected to also apply to the vibration of microelectronics assemblies. A previously proposed modification to Miner’s rule of linear damage accumulation was updated for greater accuracy, and it was explained how this circumvents the problem with the dependence of the constitutive relations on the preceding loading history. Four lead-free solder alloys were studied in varying amplitude cycling. The results showed that SAC305 is the most sensitive to variations, but it remains the most fatigue-resistant of the alloys under any single or variable amplitude conditions. SAC-X-Plus is the weakest in terms of fatigue resistance under any given combination of variable or single amplitudes. SAC105 and SAC-Ni have almost the same life under a fixed amplitude, but comparisons in variable amplitude cycling depend on the specific loading conditions.

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ACKNOWLEDGEMENT This research was supported by the National Science Foundation under Grant No. DMR 1206474, by the U.S. Department of Defense through the Strategic Environmental Research and Development Program (SERDP), and by the AREA Consortium. Solder spheres were provided by Alpha Advanced Materials. REFERENCES 1. J. Warren and Y. Wei, Int. J. Fatigue 32, 1853 (2010). 2. J. Wertz, C. Holycross, H. Shen, O. Scott-Emuakpor, T. George, and C. Cross, J. Eng. Mater. Technol. 135, 031008-1 (2013). 3. S. Chang, T. Pimbley, and D. Conway, Exp. Mech. 8, 133 (1968). 4. S. Vaynman and A. McKeown, IEEE Trans. Compon. Hybrids Manuf. Technol. 16, 317 (1993). 5. L. Yin, L. Wentlent, L. Yang, B. Arfaei, A. Qasaimeh, and P. Borgesen, J. Electron. Mater. 41, 241 (2012). 6. G. Cuddalorepatta, A. Dasgupta, and K. Holdermann, Proc. IMECE (Boston, MA, 2008). 7. A. Mayyas, L. Yin, and P. Borgesen, Proceedings of the ASME International (IMECE2009-12749, 2009). 8. K. Korhonen, L. Lehman, M. Korhonen, and D. Henderson, J. Electron. Mater. 36, 173 (2007). 9. B. Arfaei, Y. Xing, J. Woods, J. Wolcott, P. Tumne, P. Borgesen, and E. Cotts, Proceedings of ECTC (2008), pp. 459–465. 10. A. Qasaimeh, Y. Jaradat, L. Wentlent, L. Yang, L. Yin, B. Arfaei, and P. Borgesen, Proceedings of 61st ECTC (2011), pp. 1775–1781. 11. P. Borgesen, S. Hamasha, M. Obaidat, V. Raghavan, X. Dai, M. Meilunas, and M. Anselm, Microelectron. Reliab. 53, 1587 (2013). 12. M.A. Miner, J. Appl. Mech. 12, A159 (1945). 13. P. Borgesen, L. Yang, B. Arfaei, L. Yin, B. Roggeman, and M. Meilunas, Proc. SMTA Pan Pacific Microelectronics Symposium (2011). 14. L. Yang, V. Raghavan, B. Roggeman, L. Yin, and P. Borgesen, On the Complete Breakdown of Miner’s Rule for Lead Free BGA Joints (San Diego, CA: SMTA International, 2009), p. 152. 15. L. Yang, L. Yin, B. Arfaei, B. Roggeman, and P. Borgesen, IEEE Transactions on Components and Packaging Technologies (2013), pp. 430–440. 16. M. Obaidat, S. Hamasha, Y. Jaradat, A. Qasaimeh, B. Arfaei, M. Anselm, and P. Borgesen, Proc. 63rd ECTC (2013). 17. D. Henderson, J. Woods, T. Gosselin, J. Bartelo, D. King, T. Korhonen, M. Korhonen, L. Lehman, E. Cotts, S. Kang, P. Lauro, D. Shih, C. Goldsmith, and K. Puttlitz, J. Mater. Res. 19, 1608 (2004). 18. D. Dutta, J. Electron. Mater. 32, 201 (2003). 19. L. Lehman, R. Kinyanjui, J. Wang, Y. Xing, L. Zavalij, P. Borgesen, and E. Cotts, Proc. ECTC (2005) pp. 674–681. 20. T. Bieler, P. Borgesen, Y. Xing, L. Lehman, and E. Cotts, Pb-Free and RoHS-Compliant Materials and Processes for Microelectronics (MRS Spring Meeting, April 2007). 21. T. Bieler, H. Jiang, L. Lehman, T. Kirkpatrick, E. Cotts, and B. Nandagopal, Proc. Electronic Components and Technology Conference (2008), pp. 370–381. 22. L. Lehman, Y. Xing, T. Bieler, and E. Cotts, Acta Mater. 58, 3546 (2010). 23. L. Yang, L. Yin, B. Roggeman, and P. Borgesen, Proc. 60th ECTC (2010), pp. 1518–1523. 24. M. Matin, W. Vellinga, and M. Geers, Mater. Sci. Eng. A431, 166 (2006). 25. L. Kaechele, Review and Analysis of Cumulative-FatigueDamage Theories. RM-3653-PM (Santa Monica, CA: The Rand Corporation, 1963). 26. J. Grover, Symposium of Fatigue of Aircraft Structures, Presented at the third Pacific area national meeting (San Francisco, CA, October 1959).

4484 27. F. Shanley, A Theory of Fatigue Based on Unbonding During Reversed Slip (The Rand Corporation, 1952). 28. A. Shu, H. Huang, Y. Liu, L. He, and Q. Liao, Int. J. Turbo Jet Engines 29, 79 (2012). 29. H. Corten and T. Dolan, International Conference on Fatigue of Metals (Institution of Mechanical Engineers and American Society of Mechanical Engineers, 1956). 30. H. Liu and H. Corten, Fatigue Damage Under Varying Stress Amplitudes (NASA, 1960).

Hamasha, Jaradat, Qasaimeh, Obaidat, and Borgesen 31. A. Freudenthal and R. Heller, J. Aerosp. Sci. 26, 431 (1959). 32. Y. Jaradat, J. Owens, A. Qasaimeh, B. Arfaei, L. Yin, M. Anselm, and P. Borgesen, Proc. SMTA International (2012). 33. Y. Jaradat, J. Chen, J. Owens, L. Yin, A. Qasaimeh, L. Wentlent, B. Arfaei, and P. Borgesen, Proc. ITHERM 2012, pp. 740–744. 34. D. Kececioglu and B. Sun, Environmental Stress Screening: Its Quantification, Optimization and Management (Lancaster, PA: DEStech, 2003).