Determining elastic modulus from dynamic mechanical analysis data: Reduction in experiments using adaptive surrogate modeling based transform

Xianbo Xu, Nikhil Gupta

Research output: Contribution to journalArticle

Abstract

A transform was proposed in the earlier work to convert the frequency domain storage modulus obtained from dynamic mechanical analysis (DMA) to elastic modulus over a wide range of temperatures and strain rates (Polymer, 2016, 101, 1–6) from testing of a single specimen. However, the method still required conducting temperature and frequency sweeps in DMA experiments. The present work is focused on developing an adaptive DMA experimental scheme for achieving further reduction in experimentation required to characterize a material using adaptive design of experiments (DoE) method. First, the surrogate model is established based on time-temperature superposition principle using the Particle Swarm Optimization. Then four sampling methods are used to fit the data on the surrogate model. The Sobol Quasi Monte Carlo (QMC) method converges faster and has better accuracy than other methods. Then, using integral relations of viscoelasticity, the surrogate model is transformed to time domain for obtaining a temperature dependent relaxation function from which the strain rate sensitive elastic modulus is extracted and validated with tensile test results. The error is found to be below 3.9% for 5% magnitude of noise and 4.4% for 10% magnitude of noise in the strain rate range 10−5 to 10−2 s−1 using Sobol QMC method. The close agreement indicates that the adaptive DMA scheme can significantly reduce the time and cost involved in materials characterization and eliminate the need for tensile tests for measuring material modulus.

Original languageEnglish (US)
Pages (from-to)166-171
Number of pages6
JournalPolymer
Volume157
DOIs
StatePublished - Nov 21 2018

Fingerprint

Dynamic mechanical analysis
Data reduction
Elastic moduli
Strain rate
Monte Carlo methods
Experiments
Temperature
Viscoelasticity
Design of experiments
Particle swarm optimization (PSO)
Polymers
Sampling
Testing
Costs

Keywords

  • Adaptive design of experiment
  • Dynamic mechanical analysis
  • Modulus
  • Surrogate model
  • Viscoelastic properties

ASJC Scopus subject areas

  • Organic Chemistry
  • Polymers and Plastics
  • Materials Chemistry

Cite this

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title = "Determining elastic modulus from dynamic mechanical analysis data: Reduction in experiments using adaptive surrogate modeling based transform",
abstract = "A transform was proposed in the earlier work to convert the frequency domain storage modulus obtained from dynamic mechanical analysis (DMA) to elastic modulus over a wide range of temperatures and strain rates (Polymer, 2016, 101, 1–6) from testing of a single specimen. However, the method still required conducting temperature and frequency sweeps in DMA experiments. The present work is focused on developing an adaptive DMA experimental scheme for achieving further reduction in experimentation required to characterize a material using adaptive design of experiments (DoE) method. First, the surrogate model is established based on time-temperature superposition principle using the Particle Swarm Optimization. Then four sampling methods are used to fit the data on the surrogate model. The Sobol Quasi Monte Carlo (QMC) method converges faster and has better accuracy than other methods. Then, using integral relations of viscoelasticity, the surrogate model is transformed to time domain for obtaining a temperature dependent relaxation function from which the strain rate sensitive elastic modulus is extracted and validated with tensile test results. The error is found to be below 3.9{\%} for 5{\%} magnitude of noise and 4.4{\%} for 10{\%} magnitude of noise in the strain rate range 10−5 to 10−2 s−1 using Sobol QMC method. The close agreement indicates that the adaptive DMA scheme can significantly reduce the time and cost involved in materials characterization and eliminate the need for tensile tests for measuring material modulus.",
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author = "Xianbo Xu and Nikhil Gupta",
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AU - Xu, Xianbo

AU - Gupta, Nikhil

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N2 - A transform was proposed in the earlier work to convert the frequency domain storage modulus obtained from dynamic mechanical analysis (DMA) to elastic modulus over a wide range of temperatures and strain rates (Polymer, 2016, 101, 1–6) from testing of a single specimen. However, the method still required conducting temperature and frequency sweeps in DMA experiments. The present work is focused on developing an adaptive DMA experimental scheme for achieving further reduction in experimentation required to characterize a material using adaptive design of experiments (DoE) method. First, the surrogate model is established based on time-temperature superposition principle using the Particle Swarm Optimization. Then four sampling methods are used to fit the data on the surrogate model. The Sobol Quasi Monte Carlo (QMC) method converges faster and has better accuracy than other methods. Then, using integral relations of viscoelasticity, the surrogate model is transformed to time domain for obtaining a temperature dependent relaxation function from which the strain rate sensitive elastic modulus is extracted and validated with tensile test results. The error is found to be below 3.9% for 5% magnitude of noise and 4.4% for 10% magnitude of noise in the strain rate range 10−5 to 10−2 s−1 using Sobol QMC method. The close agreement indicates that the adaptive DMA scheme can significantly reduce the time and cost involved in materials characterization and eliminate the need for tensile tests for measuring material modulus.

AB - A transform was proposed in the earlier work to convert the frequency domain storage modulus obtained from dynamic mechanical analysis (DMA) to elastic modulus over a wide range of temperatures and strain rates (Polymer, 2016, 101, 1–6) from testing of a single specimen. However, the method still required conducting temperature and frequency sweeps in DMA experiments. The present work is focused on developing an adaptive DMA experimental scheme for achieving further reduction in experimentation required to characterize a material using adaptive design of experiments (DoE) method. First, the surrogate model is established based on time-temperature superposition principle using the Particle Swarm Optimization. Then four sampling methods are used to fit the data on the surrogate model. The Sobol Quasi Monte Carlo (QMC) method converges faster and has better accuracy than other methods. Then, using integral relations of viscoelasticity, the surrogate model is transformed to time domain for obtaining a temperature dependent relaxation function from which the strain rate sensitive elastic modulus is extracted and validated with tensile test results. The error is found to be below 3.9% for 5% magnitude of noise and 4.4% for 10% magnitude of noise in the strain rate range 10−5 to 10−2 s−1 using Sobol QMC method. The close agreement indicates that the adaptive DMA scheme can significantly reduce the time and cost involved in materials characterization and eliminate the need for tensile tests for measuring material modulus.

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