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September 1997

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Subject:
From:
"Andrew J. Scholand" <[log in to unmask]>
Reply To:
Date:
Thu, 4 Sep 1997 15:49:12 -0400
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I'm not sure how detailed you want your material model to be.  A fellow
student working in the Packaging Research Center digitized a series of
non-linear stress-strain curves for electro-deposited copper at different
temperatures to get a *really* accurate model.  (He has since graduated,
but if you contact Dr. Suresh Sitaraman, [log in to unmask],
I'm sure he can tell how much of that work is in the public domain.)

The following is a isotropic, nonlinear stress-strain relationship
published by Dasgupta and Ramappan in the ASME Journal of Electronic
Packaging which appears to be pretty close to the values posted to this
list by Andy Magee.

I can't do greek letters, so I'll use the quantity names instead:

Strain = stress/E + {stress/K}^(1/n)

E = 17.5 x 10^6 psi
Poissons ratio = 0.35
K = 9.2 x 10^4 psi
n = 0.15

And Fatigue information, in case you're interested:
Ultimate strength = 45,000 psi
Fatigue ductility = 17%

A couple of caveats:
1) This model assumes isotropic properties, which is a common assumption
among those who model EP problems.  However, some pretty accurate
measurements (using a laser extensometer in a temperature controlled oven)
by one of the labs here on campus has shown copper foil has at least
orthotropic properties.  To my knowledge they have not tried to relate
these to microscopic features such as grain size or distribution.

2) These are 'average' properties.  According to other posters to this
list, there are wide fluctuations in 'as delivered' material properties.
 If you search the Technet archive, Werner Engelmaier among others has had
some interesting things to say on this topic.


Hope it helps,
        Andy

REFS:
        Dasgupta, A. and Ramappan, V.  "Simulation of the Influence of
Manufacturing Quality on Reliability of Vias"  Journal of Electronic
Packaging, Vol. 117, June 1995, pp.141-146.
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