In printed circuit board assemblies, repeated temperature cycling can produce fatigue damage and eventual open-circuit failure in solder joints. The Norris-Landzberg model relates solder-joint fatigue life to cycling frequency, temperature range and maximum cycle temperature.

This article analyses generated accelerated-test data for a lead-free solder joint. The General Log-Linear (GLL) relationship in FreeWeibull.com is used to estimate the Norris-Landzberg model parameters and calculate an acceleration factor between test and use conditions.

The Norris-Landzberg relationship for the number of cycles to failure is:

where:

• N_f: number of cycles to failure
• C: coefficient
• f: cycling frequency (cycles/day)
• ΔT: temperature range during a cycle (K)
• T_max: maximum temperature during each cycle (K)
• E_a: activation energy (eV)
• K (= 8.617 x 10^-5 eV/K): Boltzmann's constant
• m, n: empirical exponents

The model accounts for three stresses that affect solder-joint fatigue life:

• Cycling frequency, f - represented by an Inverse Power Law (IPL) relationship
• Temperature range, ∆T - also represented by an Inverse Power Law (IPL) relationship
• Cycle maximum temperature, T_max - represented by an Arrhenius relationship

The acceleration factor (AF), defined here as life at the use condition divided by life at the accelerated condition, is:

The General Log-Linear (GLL) model expresses the stress-dependent life parameter L as a function of three stresses:

In FreeWeibull, L is η for a Weibull distribution or the median life for a Lognormal distribution. When the distribution shape or spread is common across stress groups, other life percentiles follow the same acceleration factor.

To align the GLL relationship with the Norris-Landzberg model, apply the following transformations:

X₁=ln(f)

X₂=ln(∆T)

X₃=1/T_max

These transformations give:

Comparison with the Norris-Landzberg equation gives the following parameter relationships:

• C = e^α0
• m = -α₁
• n = -α₂
• E_a/K =α₃

This example uses a three-stress GLL relationship for a particular lead-free solder joint. Four distinct temperature-cycling stress combinations are analysed, with 10 units per combination and inspections every 100 cycles. Because the GLL relationship contains four coefficients (α0 through α3), four distinct stress combinations are the mathematical minimum required to identify them. Additional combinations and replication are normally desirable for assessing model adequacy and experimental variability.

Life is assumed to follow a Lognormal distribution. Cycling frequency f and temperature range ΔT use Inverse Power Law relationships, while maximum temperature T_max uses an Arrhenius relationship, as shown in Figure 2.

The fitted GLL coefficients give the following Norris-Landzberg parameters:

• C = e^α0 = 56,387
• m = -α₁ = 0.2955
• n = -α₂ = 1.789
• E_a/K = α₃ = 1419

The resulting acceleration-factor relationship for this lead-free solder joint is:

Consider an accelerated test conducted at the following stress settings:

Assume that the estimated mean life at these accelerated conditions is 1,500 cycles.

Using the acceleration-factor relationship gives:

The calculated acceleration factor is 8.79. The projected mean life at the use conditions is therefore 1,500 × 8.79 = 13,185 cycles.

The projected life is conditional on the selected model and test design. Before using it for an engineering decision, confirm that:

• The same failure mechanism dominates at the accelerated and use conditions.
• The selected stress transformations are physically appropriate, and absolute temperatures are entered in kelvin.
• The common distribution shape or spread assumption across stress groups is reasonable.
• The use condition is not so far outside the tested range that the extrapolation becomes unsupported.
• Uncertainty arising from the data, model form and stress estimates is considered when interpreting the result.

This example demonstrates how accelerated life test data can be used to estimate a Norris-Landzberg relationship for solder-joint open-circuit failure caused by temperature cycling. A similar GLL formulation can be applied to other multi-stress acceleration models, such as Hallberg-Peck, when their failure physics and assumptions are appropriate.

Try the Accelerated Life Test Analysis module at FreeWeibull.com and view the FreeWeibull user guide.

K. C. Norris and A. H. Landzberg, "Reliability of Controlled Collapse Interconnections," IBM Journal of Research and Development, 13(3), 1969, pp. 266–271.