Smart Wearables
Cracks accumulate faster than washes do. A trace that looked healthy at twenty cycles can be open at forty, with nothing in between to warn you.
— Ω
Trace resistance at the completed cycle count
A negative cycles-remaining means the trace is already past the threshold, not that the model has broken. The power law is empirical and both constants must be fitted from a wash trial on the actual ink, substrate and encapsulation — they are not transferable between constructions, and encapsulation in particular changes the exponent rather than merely shifting the curve. Resistance also under-reports damage on a heated or current-carrying trace, where the added dissipation shown here concentrates at the cracks and accelerates the next failure.
Conductive Trace Wash-Cycle Fatigue & Resistance Growth — free, with the formula and a worked example, at Textile School.