Hysteresis Loop Area Thixotropy Calculator

Calculator Inputs

Enter equal-length lists for shear rate, ramp-up stress, and ramp-down stress. Values may be separated by commas, spaces, or new lines.

For thixotropic materials, a flow-curve hysteresis loop is often measured using shear stress τ versus shear rate γ̇. The loop area is estimated from the difference between the ramp-up and ramp-down curves.

• Define the stress difference at each point: Δτ(γ̇) = τup(γ̇) - τdown(γ̇)
• Trapezoidal loop area over the sweep: A ≈ ∑ 0.5(Δτi + Δτi+1)(γ̇i+1 - γ̇i)
• Reported magnitude uses |A|. The signed value depends on ordering.

Note: With τ–γ̇ curves, the area unit is stress × (1/time). It is a practical thixotropy index, not an energy density.

1. Collect paired ramp-up and ramp-down flow curves at the same shear rates.
2. Paste shear rates in increasing order into the first box.
3. Paste ramp-up stresses and ramp-down stresses with matching lengths.
4. Set unit labels for display, then apply conversion factors if needed.
5. Click Calculate to see results above the form.
6. Use Download CSV or Download PDF for reporting.

This example typically yields a positive loop area because the up curve is higher.

• Keep temperature and sample history consistent across runs.
• Use identical shear-rate grids for up and down curves.
• Increase point density near transitions for better integration accuracy.
• Report the sweep range and ramp duration alongside the loop area.

Thixotropy is a time-dependent change in viscosity caused by microstructural breakdown and recovery. A practical way to quantify it is to run an up-and-down shear-rate sweep and measure the hysteresis loop. This calculator integrates the stress gap between the two curves to produce a consistent comparison index.

During the ramp-up, structure can resist flow, giving higher stress at the same shear rate. On ramp-down, the structure may be partially broken, so stress is often lower. The separation depends on material chemistry, temperature, and the ramp protocol used.

The loop area is the integral of the stress difference versus shear rate. Larger areas generally indicate stronger time-dependent effects within the chosen sweep window. The average stress difference, computed as area divided by shear-rate range, is a convenient “single-number” summary.

Many rheology protocols span low to high shear rates (for example, decades of 1/s values) to capture both yielding and steady flow. Using 15–40 points per ramp often improves trapezoidal integration. Add more points near rapid curvature changes to reduce numerical error.

The shear-rate list must be strictly increasing and aligned across both ramps. If the down curve is sampled on a different grid, interpolate first. Remove obvious spikes caused by slip or instrument torque limits, because a single outlier can dominate the integrated area.

This tool reports both signed and absolute area. The sign depends on how the difference is defined and the ordering of curves. For comparisons across tests, normalization helps: use area per shear-rate range or area per maximum shear rate to reduce dependence on sweep width.

Two sweeps with the same endpoints can produce different loop areas if the ramp duration changes. Longer ramps allow more recovery, often shrinking the gap. If you enter a ramp duration, the calculator also reports a duration-scaled index (area × time) for protocol-to-protocol comparisons.

Report the shear-rate minimum and maximum, number of points, ramp duration, temperature, and geometry. Include the loop area magnitude and the chosen normalization. If comparing formulations, keep the same pre-shear and rest time. Attach the exported table so reviewers can trace the integration directly.

1) What does a larger loop area mean?

It usually indicates stronger time-dependent structure change during the sweep. Interpret it only within the same protocol, temperature, and shear-rate range.

2) Why must shear rate be strictly increasing?

The trapezoidal integration assumes ordered x-values. If shear rates repeat or decrease, the computed area can be wrong or even cancel artificially.

3) Can I use viscosity instead of stress?

Yes, if both ramps use the same shear-rate grid. Replace stress with apparent viscosity and interpret the area as a viscosity-based thixotropy index.

4) How many points are enough for accurate area?

More points improve accuracy, especially near sharp changes. As a practical start, use at least 15 points per ramp and increase density where curves bend strongly.

5) What if my down-curve shear rates differ?

Interpolate one curve onto the other curve’s shear-rate grid before using the calculator. Misaligned grids can bias the stress difference and the integrated area.

6) Do unit labels affect the calculation?

Labels are for display only. Use the conversion factors if your input units differ from your reporting units, so the integrated area matches your intended scale.

7) Is loop area an energy value?

No. With stress versus shear-rate data, the unit is stress times (1/time). It’s a comparative thixotropy index rather than a physical energy density.