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Temperature Dependent Deformation

Temperature Dependent Deformation

In a nonhomogeneous rod made up of steel and brass, restrained at both ends and subjected to a temperature change, several steps are involved in calculating the stress and compressive load. Due to the problem's static indeterminacy, one end support is disconnected, allowing the rod to experience the temperature change freely. Next, an unknown force is applied at the free end, triggering deformations in the rod's steel and brass portions. These deformations are then calculated and added together...

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As discussed in previous lessons, strain energy in a material is the energy stored when it is elastically deformed, a concept crucial in materials science and mechanical engineering. This energy results from the internal work done against the cohesive forces within the material. When a material undergoes shearing stress and corresponding shearing strain, the strain energy density, which is the energy stored per unit volume, is calculated. Within the elastic limit, where the stress is...

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Updated: May 25, 2026

High Speed Sub-GHz Spectrometer for Brillouin Scattering Analysis

High Speed Sub-GHz Spectrometer for Brillouin Scattering Analysis

Published on: December 22, 2015

BOTTS: broadband optimized time-temperature superposition for vastly accelerated viscoelastic data acquisition.

Richard J Sheridan¹, Stefan Zauscher¹, L Catherine Brinson¹

¹Thomas Lord Department of Mechanical Engineering and Materials Science, Duke University, Durham, North Carolina, USA. richard.sheridan@duke.edu.

|September 11, 2024

Summary

This study introduces a faster method for analyzing viscoelastic materials. By using chirp sweeps instead of discrete frequency sweeps, researchers can generate master curves significantly quicker, accelerating materials design.

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Area of Science:

Materials Science
Polymer Science
Rheology

Background:

Modern materials design relies on large datasets and complex algorithms.
Viscoelastic materials pose challenges due to time-dependent properties, slowing data collection.
Traditional time-temperature superposition (TTS) methods using discrete frequency sweeps (DFS) are time-limited.

Purpose of the Study:

To develop a faster method for generating master curves for viscoelastic materials.
To overcome the speed limitations of traditional DFS-TTS techniques.
To improve data acquisition rates in materials characterization.

Main Methods:

Utilized windowed chirp rheometry to collect simultaneous complex modulus data across three decades.
Developed a new technique called Binary Overlap Time-Temperature Superposition (BOTTS).
Employed linear error propagation and noise-weighted least squares for data analysis and shifting.

Main Results:

Achieved a ~500% increase in data collection rate compared to DFS-TTS.
BOTTS successfully superposed isothermal chirp responses to create master curves rapidly.
Demonstrated comparable results between BOTTS and DFS-TTS for model thermoset polymers.

Conclusions:

BOTTS offers a significant speed improvement for master curve generation.
This method represents a crucial advancement for accelerating viscoelastic materials characterization.
BOTTS is compatible with unmodified rheological measurement instruments.