Nonlinear dynamic response of a ‘flexible-and-heavy’ printed circuit board (PCB) to an impact load applied to its support contour

Abstract

Based on the developed simple and physically meaningful analytical (‘mathematical’) stress model, we evaluate some major parameters (amplitude, frequency, maximum acceleration, stresses and strains) of the response of a ‘flexible-and-heavy’ square simply supported printed circuit board (PCB) to an impact drop load applied to its support contour. The analysis is restricted to the first mode of vibrations and is carried out in application to the PCB design employed in an advanced accelerated test setup (test vehicle). This setup is aimed at the assessment of the performance, in accelerated test conditions on the board level, of packaging materials (and, first of all, BGA solder joint interconnections) subjected to dynamic (drop or shock) loading. It is anticipated that heavy masses could be mounted on the PCB to accelerate its dynamic response to an impact load. These masses are expected to be small in size, so that while changing the total mass of the board and generating significant inertia forces, they do not affect the board's flexural rigidity or its stiffness with respect to the in-plane loading. The PCB's contour is considered non-deformable, which is indeed the case in many practical situations. This circumstance, if the drop height and/or the induced inertia forces are significant, leads to elevated in-plane (‘membrane’) stresses in the PCB and, as a result of that, to the nonlinear response of the board to the impact load: the relationship between the magnitude of the load (determined by the initial impact velocity) and the induced PCB deflections becomes geometrically nonlinear, with a rigid cubic characteristic of the restoring force. The carried out numerical example, although reflects the characteristics of the PCB and loading conditions in an actual experimental setup, is merely an illustration of the general concept and is intended to demonstrate the abilities of the suggested method. Predictions based on this method agree well with the finite element analysis (FEA) data. The model can be helpful in understanding the physics of the addressed problem. The obtained results can be easily generalized, if necessary, for PCBs of different aspect ratios and with other boundary conditions, for different distributions of the added masses, etc, and applied, with adequate modifications, to PCBs in actual use conditions as well. The model can be used, along with FEA simulations, in the analysis, structural (‘physical’) design and accelerated testing of electronic systems of the type in question, and particularly of 'flexible-and-heavy' PCBs, both in accelerated tests and in actual operation conditions.

Dynamic Response of PCB Structures to Shock Loading in Reliability Tests

“…In a typical PCB shock test, displacements are significantly greater than the board thickness. In the numerical example carried out in [6], the predicted amplitude of the nonlinear vibrations is as high as 8.4 mm, while the PCB is only 1.5 mm thick. In a system drop, displacements are also significant-several times greater than board thickness.…”

“…These tests provide board strain-based design limits that are the basis for the specification documentation for the package subjected to shock tests [4][5][6][7][8]. The tested shock test board assembly consists of a board with one or more packages surface mounted on one side of the board (Fig.…”

“…A detailed analysis of the nonlinear dynamic response of a square, simply supported PCB used in an experimental setup has been recently addressed by the authors of this chapter [6]. Figure 5 illustrates the role of the in-plane (membrane) forces.…”

“…As shown in Fig. 6 [6], the role of the in-plane ("membrane") stresses and strains, when the lateral displacements of the board are not very small, becomes very important and might result in a significant increase in the total maximum stress. For example, when the deflection is equal to the PCB's thickness h, the maximum tensile stress in the PCB (this stress is caused now by both bending and tension) increases by 15% in comparison with the linear (small-displacement) case.…”

“…The principal conclusion from these tests is that the effects of membrane effects cannot be disregarded. In the numerical example carried out in the [6], the following data were obtained for the predicted stresses in the center of a square, simply supported PCB: bending stress σ b = ±3.2 kg/mm 2 , in-plane stress σ 0 = +5.4 kg/mm 2 , that is, by a factor of 1.7 greater than the maximum bending stress. This means that the stress on the convex side of the plane is as high as 8.6 kg/mm 2 , while the stress on the convex side is also a tensile one and is only 2.2 kg/mm 2 .…”