Conductive Trace Wash-Cycle Fatigue & Resistance Growth

The formula

This is the expression the tool evaluates. Every term is named underneath, with the unit it must be supplied in.

How the result is derived

Step by step, from the values you type to the figure on screen.

1. The 6 inputs are read from the form on every keystroke: Initial Trace Resistance, Working Current, Characteristic Cycles, Degradation Exponent, Wash Cycles Completed and Failure Threshold.
2. Each value is checked against the accepted range in the input table below. A value outside its range stops the calculation rather than producing a misleading figure — the results blank out and a message appears.
3. The validated values are substituted into the expression above, which resolves Resistance After Washing together with every supporting figure in one pass — no value is carried over from a previous entry.
4. The supporting outputs — Growth Ratio, Cycles to Threshold, Cycles Remaining, Added Voltage Drop and Added Dissipation — come from the same pass, so they always describe the same case as the headline figure.
5. Results are rounded for display only. The full-precision value is used throughout the chain, so reading a rounded intermediate figure back into the tool by hand can shift the last digit.

What each input means

Where to read each value on the floor, the unit it must be in, and the range the tool accepts.

What the tool returns

The headline figure and every supporting value it is built from.

Worked example

The tool loads with this case already solved — the Resistance After Washing shown above is its answer. Change one value and the difference from this baseline is the sensitivity of the result to that variable.

How to use it

1. Work through the input groups in order — Trace and Degradation Behaviour. The defaults are a realistic case, so you can change one value at a time and watch what moves.
2. There is no calculate button. Every figure recalculates as you type or drag, which is what makes this usable for a what-if sweep rather than a single answer.
3. Read Resistance After Washing in the dark results panel — that is the headline figure, expressed in Ω.
4. Check the supporting rows underneath (Growth Ratio, Cycles to Threshold, Cycles Remaining, Added Voltage Drop and Added Dissipation) before acting on the headline — they are where an implausible input usually shows itself first.
5. Reset to defaults returns every field to the reference case, which is the quickest way to check whether a surprising result came from the tool or from an input you had changed earlier.

Where this is used

• Process planning — establishing Resistance After Washing before a trial is booked, so machine time and material in E-Textiles, Smart Wearables & Biomimetics are committed against a calculated figure rather than an estimate.
• Costing and quotation — Resistance After Washing is an input to the cost sheet, and quoting from a worked number rather than a remembered one is what keeps a margin intact.
• Troubleshooting — when the floor result drifts from plan, entering the measured values (starting with Initial Trace Resistance) shows how much of the gap in Resistance After Washing each variable explains.
• Teaching and study — the accepted ranges bracket normal E-Textiles, Smart Wearables & Biomimetics practice, so moving one variable at a time shows the shape of the relationship rather than a single answer.

Assumptions and limits

• 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.
• Every input is bounded to the range normal practice occupies (Initial Trace Resistance 0.1 to 5000 Ω, Working Current 0.001 to 10 A and Characteristic Cycles 1 to 500 no., and so on for the rest). Those bounds are guard rails against typing errors, not a claim that the formula fails one unit outside them.
• The calculation is deterministic: the same inputs always give the same result. It carries no allowance for machine condition, operator skill, ambient conditions or lot-to-lot material variation unless an input above explicitly represents one.
• Nothing is sent anywhere. The maths runs in your browser, so the numbers you type never leave the page.

Questions people ask