ABAQUS中的钢的Chaboche非线性循环硬化本构用法
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1 Copyright © 2014 by ASME Proceedings of the ASME 2014 Pressure Vessels & Piping Conference
PVP2014
July 20-24, 2014, Anaheim, California, USA
PVP2014-28772
ADDITIONAL GUIDANCE FOR INELASTIC RATCHETING ANALYSIS USING THE
CHABOCHE MODEL
William F. Weitze, P.E.
Structural Integrity Associates, Inc.
San Jose, California, USA Timothy D. Gilman
Structural Integrity Associates, Inc.
San Jose, California, USA
ABSTRACT
This paper builds on PVP2013-98150 by Kalnins,
Rudolph, and Willuweit [1], which documented two calibration
processes for determining the parameters of the Chaboche
nonlinear kinematic hardening (NLK) material model for
stainless steel, and tested the material model using a
pressurized cylindrical shell subjected to thermal cycling. The
current paper examines (1) whether a Chaboche NLK model
with only two terms (rather than four as in PVP-98150) is
sufficiently accurate, (2) use of the ANSYS program for
material model refinement and finite element analysis, and (3)
analysis using temperature-dependent NLK model parameters,
again using ANSYS.
INTRODUCTION
Ratcheting is progressive distortion of a component under
cyclic duty. Taken to the extreme, it can lead to an unstable
component geometry and subsequent collapse. Section III of
the ASME Boiler and Pressure Vessel Code contains equations
to prevent ratcheting in nuclear reactor components, such as
Equations 10, 12, and 13 of NB-3650, for example [2].
Inelastic analysis is used to evaluate ratcheting when it is
necessary to remove excess conservatism. When an inelastic
analysis is performed, the design is considered acceptable if
either shakedown occurs after a few cycles, or the maximum
accumulated local strain does not exceed 5% (for certain
materials only) [2, NB-3228.4(b)]. However, the ASME Code
does not provide guidance as to how the inelastic analysis
should be performed.
A relatively simple inelastic analysis approach would be to
assume elastic-perfectly plastic behavior. However, this
approach is still significantly conservative compared to the
actual behavior of ductile materials. Work is currently
underway to develop more accurate inelastic analysis
methodology. The Chaboche NLK material model is
sufficiently sophisticated to model ratcheting behavior, but
additional work is needed to further its application to real world
problems. Paper PVP2013-98150 by Kalnins, Rudolph, and
Willuweit [1] provided guidance for ratcheting analysis using
the Chaboche NLK material model for stainless steel. This
paper continues this line of work as described in the abstract.
NOMENCLATURE
C
K = material parameter for the Kth component
E
y = modulus of elasticity
K = 1 to N, a Chaboche model component
N = number of Chaboche model components
R
p0.2 = 0.2% proof stress
= backstress
K = backstress for the Kth component
NLK = total backstress from NLK model
K = material parameter for the Kth component
= uniaxial engineering strain
p = uniaxial plastic engineering strain
true = uniaxial true strain
= engineering stress
0 = initial yield stress at the elastic limit
true = true stress
uts = ultimate tensile strength
ys = yield strength
DEVELOPMENT OF CHABOCHE MODEL
PARAMETERS
As in PVP2013-98150, the Chaboche model is based on
the monotonic stress-strain curve obtained from a tension
specimen subjected to uniaxial loading [1, Section 3.1]. This is
conservative because it neglects the beneficial cyclic hardening
that occurs with stainless steels. Specific curves are taken from
ASME Code Section VIII, Division 2, Annex 3-D, paragraph 3-
D.3 [2], for SA-312 TP304 at 400°F as was previously done [1,
Section 3.2], as well as the 70°F curve from the same source.
Table 1 shows selected properties for these curves.
Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 11/25/2014 Terms of Use: http://asme.org/terms 2 Copyright © 2014 by ASME Table 1: Selected Properties of SA-312 TP304
at 70°F,
in ksi at 70°F,
in MPa at 400°F,
in ksi at 400°F,
in MPa
uts 75.0 517.10 64.0 441.26
ys 30.0 206.84 20.7 142.72
E
y 28300 195119 26400 182019
As before, the true stress-true strain curve from Section
VIII-Division 2 is converted to engineering stress-engineering
strain for the calibration as follows [1, Section 3.2]:
= exp(
true) – 1 (1)
=
true/(1 + ) (2)
Figure 1 shows the two stress-strain curves after
conversion, and Figure 2 shows the portion of the curves used
in the current analysis.
Figure 1: Engineering Stress-Engineering Strain
Curves Based on Section VIII Division 2
Figure 2: Curves Up to 5% Engineering Strain As before, the initial yield stress at the elastic limit,
