The power law for modeling cyclic elastoplasticity and viscoelasticity
Date Issued
2004
Date
2004
Author(s)
DOI
922211E002078
Abstract
The present project was proposed to study in a two-year period common characteristics and basic
principles underpinning viscoelasticity and elastoplasticity. The power law is specifically introduced
into the stress-strain relationship by converting the power law to the fractional derivative and to the
kernel of the stress functional of the plastic strain increment.
We studied various constitutive models of non-aging linear viscoelasticity. These include 3 kinds of
non-parametric models: integral constitutive laws, distributed Kelvin and Maxwell models, and
distributed fractional Kelvin and Maxwell models, and also 6 kinds of parametric models: differential
constitutive laws, generalized Kelvin and Maxwell models, distributed Kelvin and Maxwell models of
a variety of special distributions, state space methods, fractional derivative constitutive models, and
distributed fractional Kelvin and Maxwell models of a variety of special distributions. In view of the
role the integral constitutive laws play as a framework for constructing and uniting various forms of
constitutive modeling, we went further to investigate their 16 expressions, generalizing them from
non-aging linearity to aging linearity, and furthermore to a general expression for aging nonlinarity.
Ratchetting behavior is one of the most difficult phenomena to model among the viscoelastic and
elastoplastic stress-strain relations. Generally speaking, ratchetting can be found under cyclic loading
with non-zero mean stress. However, some experiments showed that even under cyclic loading with
zero mean stress, ratchetting in the direction of tension can still be found. The experimental part of this
project analyzed the phenomena of ratchetting under nominal-stress -controlled cyclic loading and
true-stress-controlled cyclic loading with zero mean stress. The results show that ratchetting in the
direction of tension can be found in true-stress-controlled experiments as well as in
nominal-stress-controlled experiments.
The results of analysis also show that the ratchetting in the direction of tension as mentioned above was
caused by the asymmetry of hardening between tension and compression, the hardening of
compression being larger than the hardening of tension and hence the tensile strain being larger than
the compressive strain in each cycle. As the cyclic contributions accumulated, the ratchetting in the
direction of tension gradually developed. Furthermore, the difference of controlled path would also
affect the asymmetry of hardening between tension and compression. If the controlled path started in
the compression direction, the asymmetry of hardening between tension and compression would be
more apparent than that of the controlled path starting in the direction of tension; therefore, ratchetting
is more apparent. For cyclic hardening materials, e.g. Al 7075, the phenomenon of ratchetting in the
direction of tension was shadowed in the first few cycles. Once the cyclic hardening effect phased out,
ratchetting manifested itself.
In order to conduct true-stress-controlled experiments, we developed formulae to calculate the
theoretical value of radial strain, and checked its accuracy by a self-developed radian strain
extensometer.
Subjects
viscoelasticity
elastoplasticity
integral constitutive laws
power law
fractional derivative
ratchetting
cyclic loading with zero mean stress
true stress control
asymmetry of hardening between tension and compression
Publisher
臺北市：國立臺灣大學土木工程學系暨研究所
Type
report
File(s)![Thumbnail Image]()
Loading...
Name
922211E002078.pdf
Size
929.32 KB
Format
Adobe PDF
Checksum
(MD5):43802571e6b4bbb07b3a577520a93e37