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**Chapter 14** 

© 2012 Kobayashi et al., licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2012 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution,

**Application of Thermo-Viscoelastic** 

**Laminated Plate Theory to Predict** 

**Warpage of Printed Circuit Boards** 

Takaya Kobayashi, Masami Sato and Yasuko Mihara

Along with rapid assembly for the purpose of creating thinner printed circuit boards, the side effect of warping during the reflow process is inevitable. As a result, the assembly process encounters serious challenges, such as difficulty in implementing a highly integrated assembly, as well as degradation in the reliability of connectivity. Aside from attempts to simulate these issues employing the FE analysis method, it is also necessary to conduct an estimation of the warpage at the early stage of design, for which development of more simplified estimation tools is strongly desired. From a material behavior point of view, if any glass transition points exist within the temperature range of the reflow process, the relaxation effect (due to viscoelastic characteristics of the material of the boards) appears as a deformation, which acts as a barrier to achieving a distinct estimation of the amount of warpage. Generally speaking, the viscoelastic behavior of resin materials exhibits very sensitive temperature dependency. This makes it difficult to accurately capture the characteristics of resin materials in actual experiments, and accordingly, to build numerical models based on such an experimental measurement. There have been many analysis cases published using sophisticated FE approaches (Shrotriya et al., 2005 and Valdevitet al., 2008),

but these approaches have not extended beyond applications as a handy design tool.

To easily estimate the thermal deformation in the laminated structure, some approaches employ the multilayered beam theory (Lim, 2008 and Yuju, 2003). The method proposed in this paper enhances these approaches to incorporate the layered plate theory, and includes the effect from the temperature-dependent viscoelasticity and the temperature-dependent coefficient of thermal expansion of resin materials. The program, which is equipped with the developed method, can give an arbitrary temperature history to a multilayered plate consisting of an arbitrary number of layers. As well, the practical approach for measurement

and reproduction in any medium, provided the original work is properly cited.

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/49978

**1. Introduction** 

