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A statistical damage-based fractional creep model for Beishan granite

A statistical damage-based fractional creep model for Beishan granite A better understanding of the creep behavior of Beishan granite is important to provide guidelines for the design and implementation of nuclear-waste repository facilities. Considering the effect of isotropic stress, damage variables describing the damage evolution in the accelerated creep stage were introduced based on the Weibull distribution of the microscopic element strength in combination with the Drucker–Prager (D–P) criterion. Based on the Abel dashpot, a statistical damage variable D\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$D$\end{document} was introduced to the order of fractional derivative to construct a nonlinear damage dashpot to describe the accelerated creep stage. Thus, with the consideration of both the viscoelastic–plastic properties and damage effects, a modified nonlinear three-dimensional model was developed to describe the creep behavior of the granite. The effectiveness of the model was verified by fitting the parameters to the experimental data for the Beishan granite creep test under triaxial loading. The results show that the modified creep model fits the experimental data better than the Nishihara model and can describe the entire creep process of rock. The influence of stress level σ\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$\sigma $\end{document}, viscosity coefficient η2\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$\eta _{2}$\end{document}, and damage variable D\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$D$\end{document} on creep deformation was revealed by sensitivity analysis. Furthermore, the order of the fractional derivative was discussed, and the order was considered to be associated with the damage state of the material, which provides a direction for the study of the physical significance of the fractional order. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mechanics of Time-Dependent Materials Springer Journals

A statistical damage-based fractional creep model for Beishan granite

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Publisher
Springer Journals
Copyright
Copyright © The Author(s), under exclusive licence to Springer Nature B.V. 2022
ISSN
1385-2000
eISSN
1573-2738
DOI
10.1007/s11043-021-09535-8
Publisher site
See Article on Publisher Site

Abstract

A better understanding of the creep behavior of Beishan granite is important to provide guidelines for the design and implementation of nuclear-waste repository facilities. Considering the effect of isotropic stress, damage variables describing the damage evolution in the accelerated creep stage were introduced based on the Weibull distribution of the microscopic element strength in combination with the Drucker–Prager (D–P) criterion. Based on the Abel dashpot, a statistical damage variable D\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$D$\end{document} was introduced to the order of fractional derivative to construct a nonlinear damage dashpot to describe the accelerated creep stage. Thus, with the consideration of both the viscoelastic–plastic properties and damage effects, a modified nonlinear three-dimensional model was developed to describe the creep behavior of the granite. The effectiveness of the model was verified by fitting the parameters to the experimental data for the Beishan granite creep test under triaxial loading. The results show that the modified creep model fits the experimental data better than the Nishihara model and can describe the entire creep process of rock. The influence of stress level σ\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$\sigma $\end{document}, viscosity coefficient η2\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$\eta _{2}$\end{document}, and damage variable D\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$D$\end{document} on creep deformation was revealed by sensitivity analysis. Furthermore, the order of the fractional derivative was discussed, and the order was considered to be associated with the damage state of the material, which provides a direction for the study of the physical significance of the fractional order.

Journal

Mechanics of Time-Dependent MaterialsSpringer Journals

Published: Jan 20, 2022

Keywords: Fractional derivative; Creep constitutive model; Statistical damage; Nonlinear damage dashpot; Beishan granite

References