The power law for modeling cyclic elastoplasticity and viscoelasticity
Date Issued
2003
Date
2003
Author(s)
DOI
912211E002077
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.
Ratchetting is one of the most difficult behavior
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 first year 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
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
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