PSI - Issue 79

Giulia Morettini et al. / Procedia Structural Integrity 79 (2026) 440–448

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By applying these displacements to a simplified clamped-beam model representing the component lead, and correlating them with the PCB resonance frequency and the excitation duration, it is possible to estimate the cumulative damage generated by these stresses. Finally, through knowledge of the lead material and its corresponding Wöhler curve, Fachri P. Nasution (2012), as well as the geometry of the terminals, a quantitative evaluation of fatigue damage due to PCB curvature can be obtained using Miner’s rule. 3.2. Calculation of the Damage Due to Component Dynamics As illustrated in Fig. 5, starting from the results obtained in the first phase of the workflow, namely the pointwise displacement PSDs of the PCB, it is possible to use these data as input for evaluating the damage associated with the dynamic behavior of the component. The underlying idea is that, by knowing the local vibrational response of the board, the dynamic behavior of an individual component can be modeled through a simplified equivalent mass–spring–damper system. In this simplified scheme, the mass represents the component body, while the spring and damper correspond respectively to the stiffness and the dissipative behavior of the connection leads’ material. All parameters required to build this model are easily obtainable from the manufacturer’s datasheet of the component to be installed. Based on this information, the model allows the determination of the relative motion between the component mass and the PCB surface, which represents the displacement experienced by the component lead during vibrational excitation. This relative motion translates directly into an alternating tensile and compressive stress applied to the terminal. As in the previous case, the resulting load cycle is periodic and cumulative, and the damage produced can be estimated by applying Miner’s rule for cumulative fatigue damage. The outcome of this second phase thus provides an assessment of the dynamic damage associated with the vibration response of the component.

Fig. 5. Equivalent mass–spring–damper model used to evaluate the dynamic response of the component and the resulting alternating stress on the leads.

3.3. Total Damage Evaluation Under the reasonable assumption of superposition of effects, the results obtained from the two previous phases can be combined to determine, at each point of the board, the total accumulated damage (Quigley et al. (2016)). The overall relationship can be expressed as: ��� � � � �� (1) where � represents the damage induced by the curvature of the board, and �� corresponds to the damage resulting from the dynamic response of the component. The outcome of this superposition allows the generation of a damage map of the PCB, as illustrated in Fig. 6, which visually highlights the areas most susceptible to fatigue.