Quick Assessment of Yield Stress in Soft Solids

Keywords: HR rheometer, Oscillatory test, yield stress, USP 1912

TB116

Abstract

Understanding yield stress and the linear viscoelastic region (LVR) is essential for characterizing soft solid products such as lotions, creams, and gels. Yield stress directly affects spreadability, stability, and user experience. The LVR is the stress range where the material’s structure remains undisturbed; the end of the LVR corresponds to the onset of structural breakdown. Guidance from USP <1912> [1] emphasizes the importance of rheological characterization for semisolid products, highlighting parameters such as yield stress as a key indicator of product quality and consistency.

Using a TA Instruments™ Discovery™ HR Rheometer, both yield stress and LVR can be determined quickly and reliably. Techniques such as amplitude sweep enable fast, high‑resolution insight into the structure and performance of soft solids, supporting efficient formulation development and QC workflows.

Introduction

The oscillatory amplitude sweep is an efficient method for determining the yield stress and assessing structural integrity in soft solids. In this test, the applied stress or strain amplitude is gradually increased while tracking the viscoelastic moduli (G′ and G″). At low amplitudes, the material remains within the linear viscoelastic region (LVR), where its structure is undisturbed. As the amplitude increases, nonlinearity appears as the internal structure begins to break down.

Yielding is commonly identified by the G′–G″ crossover, where G″ exceeds G′, marking the transition from elastic dominated behavior to viscous flow. Because many soft solids exhibit timedependent behavior, the apparent yield point and yield stress in oscillatory tests varies with frequency: higher frequencies give higher crossover stresses, while lower frequencies produce lower yield points [2].

Amplitude sweeps provide a fast, sensitive way to quantify both LVR and yield behavior for products such as lotions, creams, pastes, and gels. With an HR Rheometer, these measurements can be performed quickly and repeatably, making the technique ideal for R&D, routine formulation, and QA/QC workflows.

Experimental, Results, and Discussion

Figure 1 demonstrates how rapidly yield behavior can be characterized using oscillatory strain amplitude sweeps on two soft solid formulations. A lotion was tested from 0.01 % to 100 % strain and an after‑sun gel from 0.1 % to 1000 % strain, both at 10 points per decade, giving a full test time of only ≈ 122 s per sample. From the modulus curves, the yield point (critical strain) is identified at the G′–G″ crossover. The lotion exhibits a crossover at 41.76 % strain, while the after‑sun gel shows a much higher 177.43 % strain, consistent with its stronger network structure.

To convert this yield point into a yield stress, the data can be replotted as versus oscillation stress. As shown in Figure 2, the crossover for the after‑sun gel corresponds to a yield stress of 132.65 Pa, representing the stress required to initiate flow and disrupt the material’s structure.

Figure 1. Strain amplitude sweeps for a lotion and an after-sun gel - Yield point (critical strain)
Figure 1. Strain amplitude sweeps for a lotion and an after-sun gel - Yield point (critical strain)
Figure 2. Amplitude sweep for an after-sun gel - Yield stress
Figure 2. Amplitude sweep for an after-sun gel - Yield stress

Although amplitude sweeps are often run with 10 points per decade to produce smooth curves, this density is not always required for accurate identification of the yield point or yield stress. Figure 3 shows that using only 3 points per decade preserves the same crossover behavior while reducing total test time to under 40 seconds. This significant acceleration is especially valuable in QA/QC environments where rapid and repeatable assessment of yield properties is critical.

These tests were conducted using 1‑second conditioning and sampling times, which are sufficient for fast‑responding materials such as lotions and after‑sun gels. Although the measurements are performed within the LVR, where the structure is not being damaged, materials with slower structural relaxation may still require longer equilibration. The conditioning time may be increased to 2 seconds, though this extends the total test duration from 122 s to approximately 189 s.

For these fast‑responding materials, the HR rheometer likewise exhibits rapid responsiveness, allowing conditioning times as short as half a second (although this is generally not recommended) while still producing results near equivalent to those obtained with a 2‑second conditioning time. In this example, all 41 data points were collected in approximately 100 seconds (Figure 4).

Figure 3. Strain amplitude sweeps for an after-sun gel using 10 and 3 points per decade
Figure 3. Strain amplitude sweeps for an after-sun gel using 10 and 3 points per decade
Figure 4. Strain amplitude sweeps for an after-sun gel using 0.5 and 2 seconds as the conditioning time
Figure 4. Strain amplitude sweeps for an after-sun gel using 0.5 and 2 seconds as the conditioning time

A way to further accelerate the workflow is to automate the crossover analysis. After performing the analysis, the crossover determination can be saved as an analysis template, as shown in Figure 5.

This saved template can then be loaded into the end of test analysis. With this setup, TRIOS Software automatically identifies the G′–G″ crossover as soon as the test completes, eliminating manual post‑processing (Figure 6).

Figure 5. Applying and saving crossover analysis in TA Instruments TRIOS™ Software
Figure 5. Applying and saving crossover analysis in TA Instruments TRIOS™ Software
Figure 6. Uploading the saved template at the end of test procedure
Figure 6. Uploading the saved template at the end of test procedure

References

  1. U. Pharmacopeia, “USP 1912: Measurement of yield stress of semi‑solids,” U.S. Pharmacopeia, 2023.
  2. TA Instruments, “RH146: Core Rheometry: Yield Stress, Time-dependency, and Rheometry Tips,” [Online]. Available: https://www.tainstruments.com/pdf/literature/RH146.pdf.
  3. TA Instruments, “RH151: Yield Stress & Time-Dependency: Practical Rheology,” [Online]. Available: https://www.tainstruments.com/pdf/literature/RH151.pdf.

Acknowledgement

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TA Instruments, Discovery, and TRIOS are trademarks of Waters Corporation or its affiliates

This Technical Brief was written by Behbood Abedi, PhD.

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