Modeling the lifetime of printed silver conductors in cyclic bending with the Coffin-Manson relation

This paper discusses the modeling of the lifetime of printed conductors on a flexible substrate under cyclic bending. Roll-to-roll printed silver lines on a plastic film were exposed to cyclic strains accordant to the bending radii of 15, 20, and 30 mm, and their long-term electrical behavior was monitored in situ with four-point dc resistance measurements. By using 5%, 10%, and 20% increase in resistance as failure criteria, the lifetime of test populations was assessed utilizing the Weibull reliability analysis. Based on these results, the relationship between the applied strain and the lifetime was characterized and modeled by the Coffin-Manson equation. The Coffin-Manson relation accordant behavior for the lifetimes under various strains was also verified by confirming measurements with untapped bending radii with good results. As a conclusion, the lifetime of a printed conductor with known geometry and materials under cyclic bending was able to be modeled as a function of bending radius with the Coffin-Manson relation.