Application of thermo-viscoelastic laminated plate theory to predict warpage of printed circuit boards

The rapid assembly of printed circuit boards to meet the desired goal of thinning the board creates more complexity in the reflow process, to control the occurrence of warpage in the board. Therefore, certain methods are preferred for simply yet accurately predicting the amount of warpage inevitable in the reflow process. Responding to such a need, the study was carried out aiming to provide a specific numerical method based on the multilayered plate theory, resulting in a simple procedure capable of supplying an accurate estimation of the warped deformation of the board. 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. This program can designate a temperature-dependent viscoelasticity and temperature-dependent thermal expansion coefficient to each layer. The estimation results derived from this method were compared with the FEM analysis results and confirmed to be in good agreement. Application of this method is designed for ease of use to estimate the warpage at any stage of planning and design.