Polymeric material has been applied in electronic product extensively, especially for packaging applications, thus thermomechanical analyses for encapsulated structure are frequently encountered. However, modulus and thermally induced strain of polymeric material are not constant, but time- and temperature-dependence. For simplification of the stress constitutive models, particularly for applications on electronic packaging can be found in literature, the time-dependent behavior could be neglected. Otherwise, the property only considered as a function of temperature can achieve time saving and cost down, but to the best of the author’s knowledge, the thermomechanical analysis based on different conservation laws so far has not been studied indeed. Most of the relative studies published in literature are in strain conservation law, and recently strain–stress conservation law was formulated, so-called force-displacement incremental solution. This study has developed a stress-based conservation law regardless of derived strain and strain–stress based conservation laws for stress constitutive models applied in thermomechanical analysis; meanwhile, incorporated cross-link induced residual strain from polymer forming. Furthermore, the nonincrement approach is implemented by a concept of force and moment equilibrium on the flexural stiffness of final stage, and derived for efficiency enhancing. On the other hand, analytical solutions based on different conservation laws for bimaterial plate were utilized to compare with experimental measurements. The results indicate that warpage analysis based on stress conservation law with temperature-dependent property can be more realistically predicted over a range of temperature, whereas a large error can be caused by using approximated CTE or nonconsidering residual strain, especially for temperature above Tg.
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December 2011
Research Papers
Different Conservation Laws Constructed on Warpage Analyses for Bimaterial Plates With Temperature-Dependent Properties
Chih-Sung Chen
Chih-Sung Chen
Corporate Engineering/Advanced Semiconductor Engineering, Inc.
, 26 Chin 3rd Road, Nantze Export Processing Zone, Nantze, Kaohsiung 811, Taiwan
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Chih-Sung Chen
Corporate Engineering/Advanced Semiconductor Engineering, Inc.
, 26 Chin 3rd Road, Nantze Export Processing Zone, Nantze, Kaohsiung 811, Taiwan
J. Electron. Packag. Dec 2011, 133(4): 041006 (14 pages)
Published Online: December 9, 2011
Article history
Received:
December 2, 2010
Revised:
September 30, 2011
Online:
December 9, 2011
Published:
December 9, 2011
Citation
Chen, C. (December 9, 2011). "Different Conservation Laws Constructed on Warpage Analyses for Bimaterial Plates With Temperature-Dependent Properties." ASME. J. Electron. Packag. December 2011; 133(4): 041006. https://doi.org/10.1115/1.4005293
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