PWB deflection vs. vibration-induced solder joint deformation

Vibration-induced solder joint failure is one of the common failure modes in microelectronics used in the automotive and the aerospace industries. In most of these applications, printed wiring boards (PWBs) with multiple surface-mount components are attached to a base frame through either sockets, clamps, or receptacles. Since the base frame is typically attached to the vehicle, the vehicle´s vibration causes the PWB to vibrate. Transverse vibration of the PWB results in significant board deflection. Deflection of the PWB induces significant strain of the solder joints on the surface-mounted components. PWB deflection is one of the parameters that can be easily measured during a vibration test. Therefore, it is often used as a design parameter. Intuitively, it is plausible that larger deflection induces more strain on the solder joints, thus results in failure. However, to design the PWB and its fixture against vibration-induced solder joint failure, it is critical to understand the quantitative relationship between the deflection of the PWB and the corresponding deformation of the solder joints. In this work, a semi-analytical method is developed to calculate the strain in the solder joints for a given magnitude of PWB deflection. Input parameters to the calculations include the PWB size, mass, modulus, types of fixture, package size, solder geometry, elastic-plastic properties of the solder alloys, etc. The methodology is semi-analytical in that the solutions are given in explicit expressions and the evaluation of these expressions requires very minimum numerical computations that can be accomplished without the need for high performance computers. More importantly, these semi-analytical solutions provide a convenient way to gain deeper physical insights and the understanding of effects of various parameters, allowing the designer to test multiple “what if” scenarios quickly.