Loading Pyodide...

Polymer Fatigue Criteria Explorer

Compare a reference stress-life relation against hysteresis dissipated energy, cyclic creep strain-rate, and a hybrid energy + creep criterion for a single polymer operating point. This is an exploratory comparison tool, not a sign-off calculator.

Tool Purpose & README

What this tool does

This explorer compares multiple polymer-fatigue criteria side by side and keeps the model assumptions visible. It is built for the case where classical S-N logic is not enough and loop observables matter.

  • Preset load-case mode: estimates loop energy and cyclic creep from the selected preset and operating point.
  • Measured-loop mode: uses stabilized hysteresis energy and cyclic creep rate directly.
  • Comparison first: shows model spread, governing criterion, regime labels, and range warnings together.
  • Progressive disclosure: click a criterion row to inspect its substituted equation and current observables.

The default presets are literature-inspired and intentionally limited. If you have measured loop data, measured-loop mode is the more trustworthy comparison path.

Inputs

Expert Mode Show custom calibration inputs
Loading presets...
?
?
?
?
?
?
?
?
?
Preset load case: the tool will estimate loop energy and cyclic creep rate from the selected preset and operating point.
?
?

Custom Calibration Inputs

These fields matter when Custom calibrated polymer is selected.
?
?
?
?
?
?
?
?
?
?
?
?
?
?

Load the default example or modify the operating point, then press Calculate.

Life By Criterion

What this shows: side-by-side predicted life from each enabled criterion. Key insight: the gap between bars is often more important than any single absolute number.

Comparison Sweep

What this shows: how the compared criteria diverge as the operating point severity changes.

Calibration Envelope

What this shows: the current loop-energy / cyclic-creep point against the preset envelope.
Contents
  1. Overview
  2. Workflows
  3. Load Ratio R
  4. Compared Criteria
  5. LCF, HCF, and mechanism labels
  6. Limitations
  7. References

1. Overview

Polymer fatigue often depends on time-dependent loop evolution, not just a single stress amplitude. This tool keeps a classical reference model in view, but it is intentionally not the only story.

Design intent: comparison and intuition building. If measured stabilized loop data are available, use the measured-loop workflow instead of relying on preset-side surrogates.

2. Workflows

Preset load case

Uses the preset to estimate stabilized loop energy and cyclic creep rate from stress amplitude, load ratio, conditioning, orientation, temperature, and frequency. This is fast and useful for trend exploration, but the inferred loop observables are still model-dependent.

Measured stabilized loop

Uses direct loop energy and cyclic creep rate values. This is the preferred path when you have test or simulation outputs and want the comparison to rest on measured observables.

3. Load Ratio R

The load ratio is the standard fatigue shorthand R = sigma_min / sigma_max. It tells the tool whether the cycle is fully reversed, tension-compression, or mostly tension-tension.

Definition used by this tool $$ R = \frac{\sigma_{min}}{\sigma_{max}}, \quad \sigma_{max} = \frac{2 \sigma_a}{1 - R}, \quad \sigma_{min} = R \sigma_{max} $$
  • sigma_a: stress amplitude entered by the user
  • sigma_max, sigma_min: peak and valley stress in the fatigue cycle
  • Why it matters: changing R changes mean stress, which changes creep tendency and fatigue response in polymers
Common examples
  • R = -1: fully reversed loading, for example +50 MPa to -50 MPa
  • R = 0: pulsating tension, for example 0 MPa to +100 MPa
  • R = 0.1: tension-tension loading, for example +10 MPa to +100 MPa
  • Larger positive R: more positive mean stress, usually more important for cyclic creep and mean-stress sensitivity
If you know your peak and valley stress already: compute R = sigma_min / sigma_max and enter that value here. The tool then reconstructs the cycle from your stress amplitude and R.

4. Compared Criteria

Equation (1) Reference stress-life $$ \sigma_{max} = \frac{2 \sigma_a}{1 - R}, \quad \sigma_m = \frac{\sigma_{max} + \sigma_{min}}{2} $$ $$ \sigma_{a,ref} = \sigma_a \left(1 + k_m \frac{\max(\sigma_m, 0)}{S_{ut}} \right), \quad N_f = \frac{1}{2}\left(\frac{\sigma_{a,ref}}{\sigma_f'}\right)^{1/b} $$
  • sigma_a: stress amplitude
  • R: load ratio
  • k_m: mean-stress sensitivity used only in the reference layer
  • sigma_f', b: reference stress-life coefficients
Equation (2) Hysteresis dissipated energy $$ W_d = \oint \sigma \, d\varepsilon, \quad \log N_f = A + B \log W_d $$
  • W_d: stabilized hysteresis energy per cycle
  • A, B: preset or custom calibration constants
Equation (3) Cyclic creep strain rate $$ \log N_f = C + D \log \left( d\varepsilon_{max}/dN \right) $$
  • d epsilon_max / dN: stabilized maximum-strain evolution metric per cycle
  • C, D: preset or custom calibration constants
Equation (4) Hybrid energy + creep $$ \frac{1}{N_{hybrid}} = \frac{w_c}{N_{creep}} + \frac{1 - w_c}{N_{energy}} $$
  • w_c: creep-side weighting used by the hybrid criterion
  • N_creep, N_energy: life predictions from the two component criteria

5. LCF, HCF, and mechanism labels

The cycle-band label is only a guide. The mechanism label is often more informative because it indicates whether the current point is being organized more strongly by dissipation, by cyclic creep, or by neither alone.

Do not over-interpret compressive benefit or a single spread-free prediction. Polymer fatigue remains sensitive to conditioning, frequency, test protocol, and the exact loop metric definition.

6. Limitations

  • Constant-amplitude, uniaxial loading only.
  • No rainflow counting, dwell-fatigue sequencing, or Miner damage.
  • No multiaxial or notch-root modeling.
  • Preset load-case mode uses explicit surrogate relations. It is exploratory by design.
  • Results outside preset range are still shown, but confidence is intentionally downgraded.