Stress Relaxation Test — Relaxation Curve, Maxwell and Prony Series Fit
Paste the time and stress columns from a stress relaxation test and get σ/σ₀ against log time, the total relaxation and the relaxation per decade, and Maxwell, Prony-series and logarithmic fits compared with their standard errors — with the relaxation modulus when you give the held strain. Nothing is uploaded.
What a relaxation test measures
A relaxation test is creep turned inside out: the specimen is strained and the strain is held, and the stress needed to hold it falls with time. Most of the drop usually happens in the first minutes and the rest over days, which is why the curve is read against log time and normalised by the stress at the start, σ₀, so specimens loaded to different stresses share one axis. The page reports σ₀ and the final stress, the total relaxation in per cent, the relaxation per decade of time (the slope of σ/σ₀ on log t), and, when the held strain is given, the relaxation modulus E = σ/ε at the end of the record.
Data
Relaxation tests are a Pro tool. The preview below is fully live — every option works and you can export the figure. Pro unlocks your data.
See pricingThis is the sample dataset; every row of it can be read and copied. The plot beside it is live — change any option and watch it redraw.
| # | Specimen(opt) | Stage(opt) | Time | Axial stress | Confining pressure(opt) | Held strain(opt) | Temperature°C(opt) | |
|---|---|---|---|---|---|---|---|---|
| 1 | ||||||||
| 2 | ||||||||
| 3 | ||||||||
| 4 |
0 rows of data
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The models
The Maxwell model, σ = σ₀·e^(−t/τ), has one relaxation time and relaxes all the way to zero. Rock rarely does, which is why the Prony series — the generalised Maxwell model, σ = σ∞ + Σ σᵢ·e^(−t/τᵢ) — is the workhorse: an equilibrium stress σ∞ that is never relaxed, plus one to three exponential terms with their own relaxation times. The logarithmic law σ = σ₀·(1 − r·log₁₀(1 + t/t₀)) describes a record that relaxes at a steady rate per decade. All three are fitted by least squares to every stage and compared by r², RMSE and Akaike’s criterion; the forms are the standard viscoelastic ones (Lakes, 2009).
A Prony series will always fit better with more terms, so the page refuses terms the readings do not support. A term is dropped when its amplitude is not positive or is smaller than its own standard error, when two relaxation times are less than a factor of 1.5 apart, or when a relaxation time lies more than a decade outside the record. The figure says when this happened and how many terms were kept.
Standards
There is no ISRM suggested method and no ASTM standard for stress relaxation of rock, and the page does not pretend otherwise. The nearest standard, ASTM E328, covers stress relaxation of materials in general. The ISRM creep method explicitly leaves relaxation out. What the page does is state its method exactly — the models, how they were fitted and the rule for dropping terms — in the footer of every exported figure and in the methods paragraph below, so a reader can reproduce it.
Common questions
- How do I fit a Prony series to relaxation data?
- Choose the most terms you will allow (one to three), paste time and stress, and the page fits σ∞ and each amplitude and relaxation time by least squares, dropping any term the data cannot support. The parameters come with standard errors, and the table compares the Prony fit with a single Maxwell term and a logarithmic law.
- What is the relaxation modulus?
- The stress at a given time divided by the held strain, E(t) = σ(t)/ε. Give the held strain in its column and the page reports it at the end of each stage, in GPa for stresses in MPa.
- Is this a Pro tool?
- Yes. The page, the sample tests, every option and the figure export work for everybody. A licence lets you replace the sample with your own readings.
- Does my data leave the browser?
- No. The fits run in this tab; there is no upload and no account.
Methodology
A methods paragraph to put beside the exported figure. It describes the tool’s default settings, so edit a clause if you changed one. References are given as the tool’s source code records them.
Stress relaxation records were analysed in StrataPlot as stress against time since the strain was applied, normalised by the first reading σ₀ of each stage. Maxwell, Prony-series (up to two terms by default, a term the readings do not support being dropped) and logarithmic models after Lakes (2009) were fitted by least squares with linearised standard errors, and the relaxation per decade is the least-squares slope of σ/σ₀ on log₁₀ t.
References
- Lakes, R.S. (2009). Viscoelastic Materials. Cambridge University Press. doi:10.1017/CBO9780511626722.
- StrataPlot. (2026). StrataPlot: Stress Relaxation [Computer software]. https://www.strataplot.com/stress-relaxation-test
How to cite this tool
If a figure made here goes into a report, thesis or paper, cite the tool so readers know how it was drawn. Add the date you accessed it if your style guide asks for one.
StrataPlot. (2026). StrataPlot: Stress Relaxation [Computer software]. https://www.strataplot.com/stress-relaxation-test
@misc{strataplot_relaxation,
author = {{StrataPlot}},
title = {StrataPlot: Stress Relaxation},
year = {2026},
howpublished = {\url{https://www.strataplot.com/stress-relaxation-test}},
note = {Computer software}
}