References

PWB Warpage Information Sources

1. Sources of PWB Warpage Data

Yeh, Chao-Pin, Ume, Charles, Fulton, Robert E., Wyatt, Karl W., Stafford, John W.,
"Correlation of Analytical and Experimental Approaches to Determine Thermally Induced PWB Warpage"
IEEE Transactions on Components, Hybrids, and Manufacturing Technology, Vol. 16, No. 8, December 1993, pp. 986-994.


Daniel, I. M., Wang, T. M., Gotro, J. T.
"Thermomechanical Behavior of Multilayer Structures in Microelectronics"
Journal of Electronic Packaging, March 1990, Vol. 112, pp. 11-15.


Stitler, Michael. MS Thesis, Georgia Institute of Technology, May 1996.

2. Origins of Bimetallic Analysis Formulae

ASTM Design Formulas for BiMetallic Strips

Guyer, Eric C. (Ed)
Handbook of Applied Thermal Design.
NY: McGraw-Hill (1989).
ISBN: 0-07-025353-6


The ASTM Design formula (from ASTM standard B388, Standard Specification for Thermostat Metal Sheet and Strip) for a simply supported beam is:



where

D = deflection in inches for beams

F = flexivity in range of temperature change.

Flexivity is defined as a bulk property intrinsic to a given alloy combination in a given temperature range. The parameters of the composite combination that determine flexivity are coefficient of thermal expansion (CTE), the volume percent of each component, and the elastic modulus of each component. Since CTE is a function of temperature, so is flexivity.

= temperature change

L = free deflection length in inches

t = thickness of strip in inches



Gieck's Design Formulas for BiMetallic Strips

Gieck, Kurt and Gieck, Reiner.
Engineering Formulas. (English Translation of Technische Formelsammlung)
West Germany: McGraw Hill, Inc. (1990)
ISBN: 0-07-023455-8









ASTM-Gieck Differences

Hence, the differences between the ASTM formula and Gieck's formula are:

• the configuration of the beam- cantilever or simply supported
• the 'fudge factor' term- either 0.1325F in the ASTM formula, or in Gieck's formula
• the system of units- English units in the ASTM formula, SI in Gieck's.
• slightly different variables to represent the different quantities

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