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

Abstract

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.