Modeling the Elastic Behavior of an Industrial Printed Circuit Board Under Bending and Shear

Industrial printed circuit boards (PCBs) are nonhomogeneous and anisotropic composites consisting of copper traces, glass-reinforced epoxy laminate (FR-4), solder mask, vias, and other features. Past efforts to model the elastic behavior of PCBs involve either simplistic assumptions or complicated and detailed modeling. In this paper, a practical method that gives reasonably accurate predictions of PCB's elastic deformation is proposed. Three micromechanics models for fibrous composite, namely, the Cox-Krenchel, modified Cox lamina, and Pan, were employed in computing the mechanical properties of an industrial PCB. Copper trace orientations were accounted for in the modified Cox lamina model. A homogenization scheme based on the micromechanics models was implemented via the finite-element method to predict the board elastic bending and shear responses. Four-point bend and shear tests were conducted to verify all the three models. It was found that the models predict the bending stiffness well but overestimate its shear stiffness. In-plane strains, however, are in good agreement with the experiments.