|
This article is cited in 13 scientific papers (total in 13 papers)
Mechanics of Solids
Analysis of creep curves produced by the linear viscoelasticity theory under cyclic stepwise loadings
A. V. Khokhlov Lomonosov Moscow State University, Institute of Mechanics, Moscow, 119192, Russian Federation
(published under the terms of the Creative Commons Attribution 4.0 International License)
Abstract:
Basic qualitative properties of the creep curves generated by the linear integral constitutive relation of viscoelasticity (with an arbitrary creep compliance) under cyclic piecewise-constant uni-axial loadings (with an arbitrary asymmetry stress ratio) are studied analytically. General formulas and a number of exact two-sided bounds are obtained for maximal, minimal and ratcheting strain values during each cycle, for their sequences limits, for the rate of plastic (non-recoverable) strain accumulation and for cyclic creep curve deviation from the creep curve at constant stress which is equal to the cycle mean stress. Their dependence on loading cycle parameters and creep compliance properties are analyzed. Monotonicity and convexity intervals of cyclic creep curves, sequences of maximal and minimal strain values and ratcheting strain sequence, their evolution with cycle number growth and conditions for their boundedness, monotonicity and convergence are examined. The linear viscoelasticity theory abilities for simulation of ratcheting, creep acceleration, cyclic hardening or softening and cyclic stability under symmetric cyclic loadings are considered. The analysis carried out revealed the importance of convexity restriction imposed on a creep compliance and the governing role of its derivative limit value at infinity. It is proved that the limit value equality to zero is the criterion for non-accumulation of plastic strain, for memory fading and for asymptotic symmetrization of cyclic creep curve deviation from the creep curve at the mean stress. The qualitative features of theoretic cyclic creep curves are compared to basic properties of typical test creep curves of viscoelastoplastic materials under cyclic multi-step uni-axial loadings in order to elucidate the linear theory applicability scope, to reveal its abilities to provide an adequate description of basic rheological phenomena related to cyclic creep and to develop techniques of identification and tuning of the linear constitutive relation. In particular, it is proved that the linear constitutive relation with an arbitrary (increasing convex-up) creep compliance function provides the absence of ratcheting and cyclic softening under symmetric cyclic multi-step loadings and the absence of creep acceleration whenever a symmetric cyclic loading is added to a constant load.
Keywords:
linear viscoelasticity, cyclic creep, creep curves at piecewise-constant loading, asymmetry stress ratio, mean stress, creep acceleration, plastic strain, ratcheting, cyclic stability.
Received: March 14, 2017 Revised: May 17, 2017 Accepted: June 12, 2017 First online: July 10, 2017
Citation:
A. V. Khokhlov, “Analysis of creep curves produced by the linear viscoelasticity theory under cyclic stepwise loadings”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 21:2 (2017), 326–361
Linking options:
https://www.mathnet.ru/eng/vsgtu1533 https://www.mathnet.ru/eng/vsgtu/v221/i2/p326
|
Statistics & downloads: |
Abstract page: | 484 | Full-text PDF : | 216 | References: | 45 |
|