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(59.1)
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f(t) = Probability Distribution Function b = shape parameter (which defines the shape of the distribution) h = scale parameter (which defines the characteristic life of the distribution; this is the time in which 63.2 percent of the tested samples would fail) g = location parameter (which defines the location of the distribution in time) t = time
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Two-parameter and three-parameter distributions are commonly used to fit the temperature cycling data. The two-parameter distribution fits a straight line though the data, whereas the three-parameter distribution fits a non-linear curve through the data. In general, the two-parameter distribution is more conservative than the three-parameter distribution. Best practice is to perform regression analysis to determine which distribution best fits the data. Another important factor in the statistical assessment of test data is the confidence interval. Confidence intervals (or confidence bounds) take into account the quality of the data based on the number of samples tested.7 When two separate experimental data sets are being compared, double-sided confidence bounds are useful in normalizing the data based on the number of samples tested in each data set. An example of upper and lower confidence bounds set at 90 percent is illustrated in Fig. 59.5.
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Material Properties A tremendous number of researchers have explored the reliability of Pb/Sn solder alloys.8 A wealth of data, material properties, and proposed constitutive relationships have been captured in the literature.8, 9, 10 However, there is relatively little information in the literature on the material properties of lead-free solders. Moreover, the material property information available is on slightly different compositions of lead-free solders, with tests performed in different ways. One of the challenges with both Pb/Sn and lead-free solders is that they undergo viscoplastic deformation (creep) as a function of time, temperature, strain rate, and applied stress. A variety of creep deformation models have been used to model the viscoplastic behavior of lead-free solders. The Anand model has been successfully used to model the viscoplastic behavior of Pb/Sn solders. The model allows for the simultaneous incorporation of time-independent plastic deformation as well as time-dependent creep deformation.
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Weibull Data 1
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W2 RRX SRM MED
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F = 100 / S = 0 Data 2
W2 RRX SRM MED
F = 100 / S = 0 CB[FM]@90.00% 2-Sided B [T2]
Unreliability, F(t)
10.00 5.00
1.00 0.50
0.10 100.00 1000.00 Time, (t) 10000.00
FIGURE 59.5 A typical two-parameter Weibull distribution. The plot shows two data sets with different shape parameter (b) values but comparable characteristic life (h). Extrapolating to 1 percent failure free life shows that the 90 percent lower-bound confidential interval for data set 1 is lower than that for data set 2, even though the characteristic lives are comparable.
The functional form of the Anand model is given as shown in Eqs. 59.2 through 59.5.11, 12 m Q p = A sin h s exp kT where e p = inelastic strain rate A = experimentally determined empirical constant Q = activation energy R = gas constant x = stress multiplier s = equivalent stress s = internal state variable m = strain rate sensitivity parameter s = ho B
(59.2)
d p dt
(59.3)
s B = 1 s*
(59.4)
COMPONENT-TO-PWB RELIABILITY
d p Q dt s* = s exp A kT where
(59.5)
ho = hardening/softening constant a = hardening/softening strain rate sensitivity coefficient s* = saturation value of s for a given set of temperature and strain rate data s = saturation coefficient n = strain rate sensitivity coefficient for the saturation value of deformation resistance
The relevant material property information on the solder composition close to that recommended by iNEMI13 (Sn3.9Ag0.6Cu) is listed in Table 59.2.
TABLE 59.2 Material Properties: Anand s Constants for Lead-Free Solder Reference Solder material Strain rate range Specimens used S0 (MPa) Q/R (K) A (sec-1) x m ho S n a Pei & Qu14 95.5Sn3.8Ag0.7Cu 25 180 C 1 mm dog bone 21.57 10041 9450.6 1.1452 0.1158 133.8025 13.3372 0.0402 0.1082 Rodgers15 95.5Sn3.8Ag0.7Cu 20 125 C 4 mm dia. dog bone 24.04 11049 8.75e+06 4.12 0.23 9537 90.37 2.26e 10 1.2965 Reinikainen16 95.5Sn3.8Ag0.7Cu 1.3 9000 500 7.1 0.3 5900 39.4 0.03 1.4
One disadvantage of the Anand model is that it mainly captures steady-state creep of solder, but it does not capture primary creep (see Fig. 59.6). Since a significant portion of solder joints field life is spent in the primary creep phase, it is difficult to predict fatigue life driven by end-use conditions. In other words, although the Anand model can be successfully used in predicting the fatigue life of solder joints tested in laboratory conditions, it may not be very accurate in predicting the fatigue life of solder joints in field use conditions.What may be needed is a time-hardening creep model that can better capture primary, secondary (steady-state), and tertiary creep. Another model that proposes the incorporation of primary and tertiary creep strain rates is the A- model.17 This model proposes that the primary creep strain rate be represented as an exponential decay function of increasing creep strain, and the tertiary creep strain rate be represented as an exponential growth function of increasing creep strain. However, this model is relatively new and has not been validated with independent experimental reliability data across the industry. Other models available in the literature for different lead-free solder metallurgies are listed in Table 59.3. A more comprehensive list of mechanical material properties of lead-free solders and other materials used in electronic packages can be found in Reference 22.
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