Effective Local Flexural Stiffness of Ball Grid Array Assemblies

Parts on the circuit board serve as reinforcements and produce local stiffness, which influences the deflection of the assembly under vibration. The curvature of the circuit board, combined with material properties, produces stresses that lead to the high-cycle fatigue failure of interconnecting soldering joints. Use of a conventional finite element method (FEM)—referred to as “h-method”—for circuit board analysis is cost prohibitive, as numerous parts, each containing many soldering joints, would need to be analyzed for a typical board. Instead, a direct-stress analysis method—referred to as the multi-domain method (MDM)—can be used to calculate effective local stiffness of ball grid array assemblies. The fast and accurate MDM is based on nested multi-field displacement superposition and is similar in concept to p-type FEM. It is similar to conventional FEM only in its use of the Rayleigh-Ritz methodology. The computational advantages of MDM over conventional FEM for computing thermal stresses caused by thermal coefficient mismatch have been documented previously. In present work, the use of MDM as a direct-stress analysis method to extract the effective local stiffness of ball grid-array assemblies for determining high-cycle fatigue life has been extended. This method simulates a three-point bend test for flexural stiffness calculation. It demonstrates that the force-deflection relationship at the center of the system can be accurately achieved with proper constraints at the ends. The flexural stiffness is then calculated on the basis of beam theory. This calculation produces numerical results for various part-board connections, both with and without underfill. The accuracy of the formulation is examined for layered assembly. The results for long-layered beam theory agree with those based on layered beam theory.