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Norris-Landzberg Acceleration Transformation PWB designers typically receive a failure distribution plot (see Fig. 59.5) as part of a secondlevel package qualification report. This failure distribution plot is typically obtained in a thermal cycle oven under controlled temperature profiles that include the maximum and minimum

temperatures (Tmax and Tmin, respectively) of the thermal cycle along with the frequency ( f ) of the experimental thermal cycle. The designer must then relate these experimental data obtained under ideal conditions to a different thermal cycle condition (or conditions) encountered in the product end-use environment. Although relative comparisons of two packages thermally cycled under identical conditions can be made in a ranking sense, this type of analysis yields no information regarding the actual lifetime of the solder joints under field loading conditions. This section focuses on the mapping of a laboratory thermal cycle to different enduse thermal profiles using strain as a damage metric. 59.2.4.1 Fatigue Behavior. The fatigue behavior of many metals (including Pb/Sn and leadfree solder alloys) can be described by the Coffin-Manson relationship (Eq. 59.6),9 which relates the fatigue life of a metal to the plastic strain the material experiences during loading. Elastic strain is the reversible or recoverable deformation that occurs during a loading cycle. Plastic strain is the amount of irreversible (or permanent) deformation that occurs during a loading cycle.

where e = total strain per cycle ep = plastic portion of the cyclic strain ee = elastic portion of the cyclic strain Nf = number of cycles to failure A,B,c,m = experimentally determined empirical constants

g ,

(59.6)

Most solder joints fail in the low cycle fatigue region (less than 10,000 cycles to failure),9 where strain is primarily plastic. Thus, neglecting the elastic component of strain, Eq. 59.6 can be simplified and rearranged to yield a relationship between the number of cycles to failure and the plastic strain (see Eq. 59.7).9 Nf = ( A / p)1/ m where ep = plastic portion of the cyclic strain Nf = number of cycles to failure A,m = experimentally determined constants (59.7)

This can be further simplified to the most common form of the Coffin-Manson relationship shown in Eq. 59.8.9 Nf c p where ep = plastic portion of the cyclic strain Nf = number of cycles to failure c = an experimentally determined empirical constant (59.8)

When any metal is cycled at a temperature above 50 percent of its melting temperature (homologous temperature), the strain rates, dwell times, and maximum temperature influence its fatigue life.9 This is due to the occurrence of creep, along with plastic and elastic deformation, within these temperature regimes.9 Norris and Landzberg proposed a modified version of the Coffin-Manson relationship that considers the effects of frequency (f ) and maximum temperature (Tmax) on solder joint fatigue life (Eq. 59.9).9,10 This relationship is based on detailed physical and empirical analysis of the relationships between temperature and frequency on the thermal fatigue behavior of Pb/Sn solder alloys employed in interconnects.10 0.123 Nf = ( A / p )1.9 f 1/ 3 exp kTmax (59.9)

ep = plastic portion of the cyclic strain Nf = number of cycles to failure k = Boltzmann s constant (eV) f = cyclic frequency Tmax = maximum temperature of the thermal cycle (K) A = an experimentally determined empirical constant

59.2.4.2 Acceleration Factors. One of the challenges that must be addressed when attempting to employ Eq. 59.9 directly to assess fatigue life is the determination of the plastic strain and the value of the constant A. It is crucial to remember that the goal of this analysis is to develop an acceleration transform (or acceleration factor) that can be employed to use known fatigue-life data obtained under controlled laboratory conditions to estimate the number of cycles to failure under field conditions. The acceleration factor AF is defined as the ratio of the number of cycles to fail in the field NfF to the number of cycles to fail in the lab NfL (see Eq. 59.10). AF = where NfF NfL (59.10)

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AF = acceleration factor NfF = number of cycles to failure in the field NfL = number of cycles to failure in the lab