1. Acceleration Factor Calculation Using
Norris-Landzberg Equation
Using Accelerated Life Testing the specified Thermal Cycles can be reduced.
Accelerated Tests are performed using stresses beyond normal life cycle or usage
conditions. Accelerated tests are performed primarily to (a) identify or conform marginal
design or manufacturing areas or (b) estimate product life. Prior to initiating accelerated
testing, weak links should be investigated and potential failure modes eliminated
Reference Qualification Test Plan for the Controller, the specified Durability Thermal
Cycles for the “Flight Lifetime” are 6242 and Durability Thermal Cycles for the “
Maintenance Lifetime” are 6970
The most widely used model is the modified Coffin-Manson (Norris-Landzberg)
Equation. This can be used to determine a Acceleration Factor for the thermal test
condition and product environment. It uses: (1) an Arrhenius Term; (2) Temperature
Cycling Frequency; (3) Maximum Temperature reached in a Cycle; (4) Temperature
Range during a Cycle.
The modified Coffin-Manson (Norris-Landzberg) Equation and a worked example using
arbitrarily chosen values is shown in Page 2
Recommendation
Use appropriate Parameter (f1; f2; ∆T1; ∆T2; m; n; T1; T2; Ea ) Values for the modified
Coffin-Manson (Norris-Landzberg) Equation to suit the Controller Design and Durability
Test Requirements. Calculate Acceleration Factors for the Flight Lifetime and
Maintenance Life Time and determine the Durability Flight & Maintenance Cycles
Benefit
Durability Thermal Cycles determined using the modified Coffin-Manson (Norris-
Landzberg) Equation will be lower than using Coffin-Manson Equation, hence reduction
in Test Time and a Cost Saving
Hilaire Ananda Perera http://www.linkedin.com/in/hilaireperera
Long Term Quality Assurance

2. Modified Coffin-Manson Equation for
Acceleration Factor Calculations
For solder joint failure under thermal fatigue (temperature and frequency are
key factors), the most widely used model is the modified Coffin-Manson
equation and is given in the following forms."1" represents test environment
and the "2" represents the actual operating environment. m = 1/3, n = 1.9 ~ 2
Coffin-Manson Exponent (n)
n = 1 to 3 for Ductile Metal (e.g. solder)
n = 3 to 5 for Hard Metal Alloys / Intermetallics (e.g. Al-Au)
n = 6 to 9 for Brittle Fracture (e.g. Si & Dielectrics: SiO 2 , Si 3 N4 )
1
m n 2.5 f1 10 f2 4 ∆ T1 140 ∆ T2 125 T1 373 T2 344
3
Ea .7 Activation Energy (eV) for the failure mechanism
8.625 . 10
5
k Boltzmann's Constant (eV/deg.K)
Ea . 1 1
m n Modified Coffin-Manson (Norris-Landzberg) Equation
f2 ∆ T1 k T T
AF . .e 2 1
f1 ∆ T2
AF = 6.124 < -------- Acceleration Factor with Modified Coffin-Manson
When -----> m 0 and Ea 0
Ea . 1 1
m n
f2 ∆ T1 k T T
AF . .e 2 1
f1 ∆ T2
AF = 1.328 < --------- Acceleration Factor with Coffin-Manson
In the above equation;
f = Temperature cycling frequency (In Cycles per 24 Hour Day)
T = Maximum Temperature in Kelvins reached in a cycle
∆ T = Temperature range (in deg. C) during a cycle
AP , 24Mar03
Hilaire Ananda Perera http://www.linkedin.com/in/hilaireperera
Long Term Quality Assurance