## Coffin-Manson

One way to approach accelerated life testing is to use a model for the expected dominant failure mechanism. One such model is for solder joint low-cycle fatigue originally published by Coffin (1954) and Manson (1953), independently.

## Norris-Landzberg

Norris and Landzberg proposed the plastic strain range is proportional to the thermal range of the cyclic loading (ΔT). They also modified the equation to account for effects of thermal cycling frequency (f) and the maximum temperature( T). They and other than empirically fit the parameters for the equation.

$$ \large\displaystyle AF=\frac{{{N}_{field}}}{{{N}_{test}}}={{\left( \frac{{{f}_{field}}}{{{f}_{test}}} \right)}^{m}}{{\left( \frac{\Delta {{T}_{field}}}{\Delta {{T}_{test}}} \right)}^{-n}}\left( {{e}^{\frac{{{E}_{a}}}{k}\left( \frac{1}{{{T}_{\max ,field}}}-\frac{1}{{{T}_{\max ,test}}} \right)}} \right)$$

where,

‘field’ and ‘test’ stand for use or field and test conditions respectively.

E_{a} is the activation energy

k is Boltzmann’s constant

E_{a}/k for this equation is 1414

The fitted parameters m and n have been determined for SnPb eutectic solder to be 1/3 and 1.9 respectively. [Norris-Landzberg] A recent paper suggests the same formula and parameter values applies for lead-free (SAC) solder as well. [Vasudevan and Fan]

## What does it do?

Understanding the temperature range of the use conditions and setting up a suitable test condition, permits translating the testing results to predict the field lifetime for the solder joints.

The model provides a basis for test design and estimating the duration of the testing suitable to replicate the field lifetime duration of interest. While not perfect, it does build on a lot of excellent work accomplished previously and significantly shortens the time and expense to estimate the time to failure distribution for solder joint fatigue.

Coffin, Jr., L. F. Trans.ASME, 76, 931–950 (August 1954).

Manson, S. S. Proc. of Heat Transfer Symp., Univ. of Mich. Press. 9–76 (1953)

Norris, K C, and AH Landzberg. “Reliability of Controlled Collapse Interconnections.”* IBM Journal of Research and Development *13, no. 3 (1969): 266-271.

Vasudevan, Vasu. and Fan, Xuejun. “An Acceleration Model for Lead-Free (SAC) Solder Joint Reliability Under Thermal Cycling.”* 2008 Electronic Components and Technology Conference.*

Related:

Hypothesis un-equal variance (article)

equal variance hypothesis (article)

Reliability Growth Testing (article)

David says

Is this equation correct ? should ‘m’ be positive

Fred Schenkelberg says

In some equation presentations the field and test are inverted for this ratio, thus m would be positive. I like having the field variables on top over the test variables… for not particular reason other than I can remember the equation that way and make fewer mistakes.

Blago says

I understand the point about -m coefficient which basically “flips” the two parts of the equation.

However, I am looking at the original Norris-Landzberg article, where the (only) frequency ratio is flipped, while the temperature is not.

In some articles (e.g. Vasu Vasudevan and Xuejun Fan, “An Acceleration Model for Lead-Free (SAC) Solder Joint Reliability under Thermal Cycling “) the ratio is the same as here, while still the original Norris-Landzberg article is being quoted.

In other (e.g. Andrew E. Perkins and Suresh K. Sitaraman, “Solder Joint Reliability Prediction for Multiple Environments”) the ratio is the same as in the original article.

Any idea where this difference is coming from?

Fred Schenkelberg says

I too have noticed the different ways to express the relationship and do not know the rationale or reasons for the differences. I suspect it has to do with individual authors preferences. cheers, Fred

Jake Rivard says

In the case where the accelerated value is on top with a positive exponent, the frequency portion of the equation is stated in terms of the dwell time so…f,t = 1/tdwell,t & f,f = 1/tdwell,f.

therefore the the term then becomes (tdwell,t/tdwell,f)^(1/3) which ends up being that both the frequency term and temperature term have the test value on top with a positive exponent.

Fred Schenkelberg says

also, be careful about the ratio being exponentiated… if reverse the sign of the exponent changes.

Alfred Gregoor says

Can someone explain when you should use the Norris-Landzburg or just use the Coffin Manson?

Fred Schenkelberg says

Hi Alfred,

From what I understand Coffin Manson is a general relationship for crack propagation in metal, whereas the Norris Landzberg relationship is specific to solder joints.

hope that helps

Cheers,

Fred

Lokesh Gupta says

Second main issue with this formula is about the factor Ea/k (1414). Why the activation energy 0.121 is taken into account (0.121/0.0000862). I have never seen any Semiconductor device failure mechanism which can give Ea as 0.121.

Even the dielectric breakdown failure can have 0.2 (not below that)

Fred Schenkelberg says

Best ask Norris or Landzberg the question, yet keep in mind that they analyzed hundreds of accelerated life tests and field failure analysis reports and empirically fit the equation finding the parameters. Form of the equation using what appears to be the Arrhenius equation is a very flexible format to fit a curve, it may not have a basis in chemistry in this case. Yet there seems to a relationship related to temperature exposure to some degree. cheers, Fred

Bill Coffey says

Can the Coffin-Manson model be used to predict an adhesive joint life acceleration factor (AF)?

Fred Schenkelberg says

Hi Bill,

I would suspect the form of the equation may describe the relationship between the applied load or stress and failure, yet the constants most likely will change.

In general, for acceleration models, they were created for a specific failure mechanism and material set and range of stresses – going outside that region is likely to result in misleading results. Much better to run a multiple stress level ALT and determine the appropriate model to describe the relationship between stress and time to failure.

Cheers,

Fred

Jonathan H says

Two questions:

Have you all come across a good source for activation energies to use for different solder types (both SnPb and Pb free) that are acceptable to use for estimating AF with the Norris-Landzburg equation?

Many articles/resources I have read refer to the same fitting parameters (m and n) as shown in this article (1/3 and 1.9). Is there a good source for alternative values for n?

Fred Schenkelberg says

Hi Jonathan,

Yes, many resources use 1/3 and 1.9 along with appropriate activation energy. The fitting parameters are based on both a compilation of test data and ongoing testing of new solders and geometries. While some papers report slight variations, overall for most systems the 1/3 and 1.9 are suitable for many situations.

A literature search may reveal alternatives for your specific situation (materials and geometries and stress patterns) or it might not. You could also conduct a more elaborate set of tests to determine the fitting parameters directly, yet that will take multiple sets of stress application conditions along with sufficient samples in order to generate enough data for the regression analysis.

For activation energy, a great source is a material scientist or chemist – second is your own detailed test data, and third is a literature search. Back when I was at HP and lead-free solders were coming to market we did a lot of solder joint fatigue testing as did many others. Over time we all found that the lead-free (SAC) and tin-lead solder of old used the same set of fitted parameters in the modified Norris Landsberg model. The two solder systems have similar yet fundamentally different paths to failure (SAC needs a longer dwell to accumulate equalivant damage per cycle, for example of just one difference that affects testing) yet the N-L model remains pretty much the same.

There has been and continues to be a lot of research into solder joint fatigue, so I suspect there is new information out there that I am not aware of at the moment. So, other than general advice I do not have a good source for alternative fitting values.

cheers,

Fred

Jonathan H says

Thank you very much for the response.

Follow up question: I have observed other sources using different signs for m and n and ratios of field to test that don’t match the formula shown here. E.g. This article and other sources show (Ffield/Ftest) w/ – n and (Tfield/Ttest) w/ -m or

(Ftest/Ffield) w/ +n and (Ttest/Tfield) w/ +m

I have now found two articles that are different. Case 1: uses (Ffield/Ftest) w/ +n and (Tfield/Ttest) w/ -m. Case 2: uses (Ffield/Ftest) w/ +n and (Ttest/Tfield) w/ +m. I recognize Case 1 and Case 2 are equivalent, however Case 1 and Case 2 are not equivalent to the primary formula shown in this article.

Is there a good explanation as to why there are different ratio/signs used for different sources? Could this be an error? Am I imagining things!!?

https://web.calce.umd.edu/lead-free/SMTAI2018-Osterman.pdf

https://www.test-navi.com/eng/research/handbook/pdf/05_2_handa_C0906_en.pdf

Thanks you very much for your insights.

Fred Schenkelberg says

Hi Jonathan,

I think you are right…I went back and checked the references you mention and the original Norris and Landsberg references and a few others. It seems the paper I pulled from [Vasudevan and Fan] did have the notation incorrect.

Good catch, thanks for letting me know.

Also, the two sites you mention provide excellent examples and detailed experimental results – thanks!

cheers,

Fred