Models for physics of failures analysis during printed circuit board bending

Abstract

This paper summarizes the force calculation at each pitch position for the structure, where a component (overmold, die, and BT) is attached to a PCB (printed circuit board) through an array of solder joints with an external bending moment applied at the ends of PCB. In this paper, the results from the model proposed by E. Suhir [1] are summarized with corrections in the derivation of the equations. Details of the new model will be described including the methodology, the formulation and the simulated results. Comparisons between the two models will be made with discussions. In this new model, each solder joint between the component and the PCB is replaced by a spring with spring constant. Benefiting from the symmetry of the structure, only half of the structure needs to be considered which simplifies the formulation of the problem and saves the computation time dramatically. The variables (unknowns) to be solved are the forces exerted on each spring due to applied external bending moment. In the subsections to come, detailed derivations will be given followed by numerical results. The setup of the new model and it is essentially the same as the Cantilever-intermediate load problem. The forces exerted on each spring will be solved through a system of linearly independent equations governed by the following conditions. All the listed formulas above are for the case when the number of leads is odd. Basically, similar formulas will be used for the case when the number of leads is even. The goal in this paper will be as follows: (a) Suhir's model deals with continuous case. It is clearly seen from the simulation results of Suhir's model that all the curves are smooth no matter how many number of solder joints are involved. The only parameter that is related to the number of joints as defined by Suhir is the spring constant of the elastic attachment. In the new model, we will solve for the force at each position in a discrete sense. That is why the curves are not that smooth when the number of solder joints is small. As the number of the solder joints becomes large (or in other words, the pitch size is small), the two models yield exactly the same results. (b) Mathematically, the new model is simpler and straightforward. The only math involved is solving the linearly independent system of equations. In Suhir's model, however, the solution process starts from solving the 4th order differential equations. Although analytical solutions can be obtained, special attention has to be paid in imposing proper boundary conditions, which might not be trivial.