A time- and temperature-dependent viscoelastic model based on the statistical compatibility condition
This paper presents a novel methodology to characterize viscoelastic materials, allowing the limitations of current conventional models based on Time-Temperature-Superposition (TTS) principle to be avoided. It implies the definition of the temperature-time field, T-t, from short-term recorded relaxa...
| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2020-08-01
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| Series: | Materials & Design |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S0264127520303622 |
| _version_ | 1818205048922963968 |
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| author | A. Álvarez-Vázquez A. Fernández-Canteli E. Castillo F. Pelayo M. Muñiz-Calvente M.J. Lamela |
| author_facet | A. Álvarez-Vázquez A. Fernández-Canteli E. Castillo F. Pelayo M. Muñiz-Calvente M.J. Lamela |
| author_sort | A. Álvarez-Vázquez |
| collection | DOAJ |
| description | This paper presents a novel methodology to characterize viscoelastic materials, allowing the limitations of current conventional models based on Time-Temperature-Superposition (TTS) principle to be avoided. It implies the definition of the temperature-time field, T-t, from short-term recorded relaxation curves at different temperatures by establishing the compatibility condition between the temperature dependent relaxation modulus at given time, E(T;t), and the time dependent relaxation modulus for a given temperature, E(t;T). The solution of the resulting functional equation allows the T-t field to be analytically defined by assuming the normalized relaxation function to be a stochastic model properly identified as a survival cumulative distribution function of certain statistical families such as normal or Gumbel ones. As a result, the corresponding master curves in the T-t field for both E-t and E-T functions are directly derived over the whole range of time and temperature, preventing user's influence on the definition of the classical shift factors and the minimum overlapping requirement over time on the short-term curves. The suitability of the proposed methodology is confirmed by its application to the experimental results from a campaign of relaxation tests on commercial PVB (polyvinyl butyral) at different temperatures. |
| first_indexed | 2024-12-12T03:50:57Z |
| format | Article |
| id | doaj.art-ece3084a6fdd430ea75a69b747274dae |
| institution | Directory Open Access Journal |
| issn | 0264-1275 |
| language | English |
| last_indexed | 2024-12-12T03:50:57Z |
| publishDate | 2020-08-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Materials & Design |
| spelling | doaj.art-ece3084a6fdd430ea75a69b747274dae2022-12-22T00:39:25ZengElsevierMaterials & Design0264-12752020-08-01193108828A time- and temperature-dependent viscoelastic model based on the statistical compatibility conditionA. Álvarez-Vázquez0A. Fernández-Canteli1E. Castillo2F. Pelayo3M. Muñiz-Calvente4M.J. Lamela5Department of Construction and Manufacturing Engineering, University of Oviedo, 33203 Gijón, Spain; Corresponding author.Department of Construction and Manufacturing Engineering, University of Oviedo, 33203 Gijón, SpainRoyal Academy of Engineering, Don Pedro 10, 28005 Madrid, Spain; Royal Academy of Sciences, Valverde 24, 28005 Madrid, SpainDepartment of Construction and Manufacturing Engineering, University of Oviedo, 33203 Gijón, SpainDepartment of Construction and Manufacturing Engineering, University of Oviedo, 33203 Gijón, SpainDepartment of Construction and Manufacturing Engineering, University of Oviedo, 33203 Gijón, SpainThis paper presents a novel methodology to characterize viscoelastic materials, allowing the limitations of current conventional models based on Time-Temperature-Superposition (TTS) principle to be avoided. It implies the definition of the temperature-time field, T-t, from short-term recorded relaxation curves at different temperatures by establishing the compatibility condition between the temperature dependent relaxation modulus at given time, E(T;t), and the time dependent relaxation modulus for a given temperature, E(t;T). The solution of the resulting functional equation allows the T-t field to be analytically defined by assuming the normalized relaxation function to be a stochastic model properly identified as a survival cumulative distribution function of certain statistical families such as normal or Gumbel ones. As a result, the corresponding master curves in the T-t field for both E-t and E-T functions are directly derived over the whole range of time and temperature, preventing user's influence on the definition of the classical shift factors and the minimum overlapping requirement over time on the short-term curves. The suitability of the proposed methodology is confirmed by its application to the experimental results from a campaign of relaxation tests on commercial PVB (polyvinyl butyral) at different temperatures.http://www.sciencedirect.com/science/article/pii/S0264127520303622Viscoelastic behaviourRelaxation curvesMaster curveGumbel distributionTime-temperature superposition principle |
| spellingShingle | A. Álvarez-Vázquez A. Fernández-Canteli E. Castillo F. Pelayo M. Muñiz-Calvente M.J. Lamela A time- and temperature-dependent viscoelastic model based on the statistical compatibility condition Materials & Design Viscoelastic behaviour Relaxation curves Master curve Gumbel distribution Time-temperature superposition principle |
| title | A time- and temperature-dependent viscoelastic model based on the statistical compatibility condition |
| title_full | A time- and temperature-dependent viscoelastic model based on the statistical compatibility condition |
| title_fullStr | A time- and temperature-dependent viscoelastic model based on the statistical compatibility condition |
| title_full_unstemmed | A time- and temperature-dependent viscoelastic model based on the statistical compatibility condition |
| title_short | A time- and temperature-dependent viscoelastic model based on the statistical compatibility condition |
| title_sort | time and temperature dependent viscoelastic model based on the statistical compatibility condition |
| topic | Viscoelastic behaviour Relaxation curves Master curve Gumbel distribution Time-temperature superposition principle |
| url | http://www.sciencedirect.com/science/article/pii/S0264127520303622 |
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