Application of thermoelastic lamination theory to predict warpage of a symmetric and simply supported printed wiring board during temperature cycling

Abstract

The applicability of classical laminated plate theory to the prediction of thermally induced warpage of a printed wiring board is examined in this study. A bare, four-layer printed wiring board without traces has been constructed. The temperature-dependent mechanical properties of the board core materials have been measured. Closed form solutions of the differential equations of equilibrium for the classical lamination theory description of the board are obtained to predict warpage. The model accounts for material property change with temperature, the board's support conditions, and thermal gradients through the board thickness to assess the role of each in the warpage process. The warpage results predicted by the model are then compared to those obtained experimentally, using the shadow-moire technique in a simulated infrared reflow environment, to assess the model's accuracy.