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A fractional derivative approach to full creep regions in salt rock

A fractional derivative approach to full creep regions in salt rock Based on the definition of the constant-viscosity Abel dashpot, a new creep element, referred to as the variable-viscosity Abel dashpot, is proposed to characterize damage growth in salt rock samples during creep tests. Ultrasonic testing is employed to determine a formula of the variable viscosity coefficient, indicating that the change of the variable viscosity coefficient with the time meets a negative exponent law. In addition, by replacing the Newtonian dashpot in the classical Nishihara model with the variable-viscosity Abel dashpot, a damage-mechanism-based creep constitutive model is proposed on the basis of time-based fractional derivative. The analytic solution for the fractional-derivative creep constitutive model is presented. The parameters of the fractional derivative creep model are determined by the Levenberg–Marquardt method on the basis of the experimental results of creep tests on salt rock. Furthermore, a sensitivity study is carried out, showing the effects of stress level, fractional derivative order and viscosity coefficient exponent on creep strain of salt rock. It is indicated that the fractional derivative creep model proposed in the paper provides a precise description of full creep regions in salt rock, i.e., the transient creep region (the primary region), the steady-state creep region (the secondary region) and the accelerated creep region (the tertiary region). http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mechanics of Time-Dependent Materials Springer Journals

A fractional derivative approach to full creep regions in salt rock

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References (34)

Publisher
Springer Journals
Copyright
Copyright © 2013 by Springer Science+Business Media Dordrecht
Subject
Engineering; Continuum Mechanics and Mechanics of Materials; Mechanics; Characterization and Evaluation of Materials; Polymer Sciences
ISSN
1385-2000
eISSN
1573-2738
DOI
10.1007/s11043-012-9193-x
Publisher site
See Article on Publisher Site

Abstract

Based on the definition of the constant-viscosity Abel dashpot, a new creep element, referred to as the variable-viscosity Abel dashpot, is proposed to characterize damage growth in salt rock samples during creep tests. Ultrasonic testing is employed to determine a formula of the variable viscosity coefficient, indicating that the change of the variable viscosity coefficient with the time meets a negative exponent law. In addition, by replacing the Newtonian dashpot in the classical Nishihara model with the variable-viscosity Abel dashpot, a damage-mechanism-based creep constitutive model is proposed on the basis of time-based fractional derivative. The analytic solution for the fractional-derivative creep constitutive model is presented. The parameters of the fractional derivative creep model are determined by the Levenberg–Marquardt method on the basis of the experimental results of creep tests on salt rock. Furthermore, a sensitivity study is carried out, showing the effects of stress level, fractional derivative order and viscosity coefficient exponent on creep strain of salt rock. It is indicated that the fractional derivative creep model proposed in the paper provides a precise description of full creep regions in salt rock, i.e., the transient creep region (the primary region), the steady-state creep region (the secondary region) and the accelerated creep region (the tertiary region).

Journal

Mechanics of Time-Dependent MaterialsSpringer Journals

Published: Aug 1, 2013

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