Modeling resistance increase in a composite ink under cyclic loading

Abstract

The electrical performance of stretchable electronic inks degrades as they undergo cyclic deformation during use, posing a major challenge to their reliability. The experimental characterization of ink fatigue behavior can be a time-consuming process, and models allowing accurate resistance evolution and life estimates are needed. Here, a model is proposed for determining the electrical resistance evolution during cyclic loading of a screen-printed composite conductive ink. The model relies on two input specimen-characteristic curves, assumes a constant rate of normalized resistance increase for a given strain amplitude, and incorporates the effects of both mean strain and strain amplitude. The model predicts the normalized resistance evolution of a cyclic test with reasonable accuracy. The mean strain effects are secondary compared to strain amplitude, except for large strain amplitudes (>10%) and mean strains (>30%). A trace width effect is found for the fatigue behavior of 1-mm vs 2-mm-wide specimens. The input specimen-characteristic curves are trace-width dependent, and the model predicts a decrease in Nf by a factor of up to 2 for the narrower trace width, in agreement with the experimental results. Two different methods are investigated to generate the rate of normalized resistance increase curves: uninterrupted fatigue tests (requiring ~6-7 cyclic tests), and a single interrupted cyclic test (requiring only one specimen tested at progressively higher strain amplitude values). The results suggest that the initial decrease in normalized resistance rate only occurs for specimen with no prior loading. The minimum-rate curve is therefore recommended for more accurate fatigue estimates.

Applicability of normalized resistance rate model for predicting fatigue life and resistance evolution in composite conductive inks

“…During a cyclic stretch test, the maximum R/R 0 during each cycle, or R max /R 0 , occurs at the maximum strain value, ε max . The rate of change in R max /R 0 with cycling, or d(R max /R 0 )/dN (where N is the number of cycles), was found by Li et al [36] to be a particularly relevant parameter for characterizing R/R 0 increase with cycling. The rate d(R max /R 0 )/dN will be referred to as (R/R 0 ) ′ for shorthand.…”

“…The fatigue behavior of composite conductive inks is less well studied, with the exception of Dupont's PE874 [17,23] where cracks were found to form and continually Effective length of double trace lines deepen during cyclic loading. For that ink, Li et al [36] recently proposed a resistance rate model for predicting PE874's fatigue behavior. It is unclear whether that model/approach could be used for other composite inks with different metal flakes, binder or substrate materials.…”

“…It is unclear whether that model/approach could be used for other composite inks with different metal flakes, binder or substrate materials. For this to be explored, the electrical resistance of other inks needs to be experimentally obtained during monotonic and cyclic loading following Li's [36] process, as described below. Table 1, provides a list of symbols used in this manuscript.…”

“…A constant rate model was proposed by Li et al [36] to predict the evolution of R max /R 0 for N cycles. The model takes input parameters from several monotonic and cyclic stretch tests to create a prediction of R max/ R 0 -cycles evolution for a cyclic test with any given ε m and ε a within the modeled range, as shown by the schematic in figure 1.…”

“…The model can also be used to predict fatigue life as defined by the number of cycles until a failure threshold for R max /R 0 is reached according to the model. If failure is defined by (R max /R 0 ) fail , then the predicted fatigue life (N f ) modeled is: Inputs are the average polynomial fit for R/R0-ε from monotonic stretch tests and power law fit for (R/R0) ′ -εa from cyclic stretch tests; outputs are the predicted Rmax/R0-cycles evolution and εa-N f , as described in the work of Li et al [36].…”