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Part I. Theory report for CREEP-PLAST computer program: analysis of two- dimensional problems under simultaneous creep and plasticity

01 Jan 1972-
TL;DR: In this article, the authors considered the combined creep and plasticity problem and derived the kernel function for a particular class of material that exhibits well defined primary and secondary creep parts such as stainless steel, and the properties of the resulting stress- strain integral are discussed in relation to the direct-superposition method.
Abstract: >Solution of the combined creep and plasticity problem is considered. Both creep theories, the equation-of-state and memory theories, are used within the framework of the finite-element computatioral method. Because of the limited creep data, which is available only for single-step simple extension experiments, the integral expansion in the memory theory formulation is limited to one nonlinear superposition integral. However, instead of using direct superposition as proposed earlier, the kernel function was derived as an integral transformation that reduced the time--temperature- stress relationship to a single quantity. The equationof-state formulation is based on the monotoric strain-hardening rule app1ied to the primary creep componert only. The uniaxial stress- strain law is first discussed with emphasis on the memory theory. Then the incremental stress- strain relations for the combined creep and plasticity problem are derived for both creep theories. The time--temperature- stress transformation is derived for a particular class of material that exhibits well- defined primary and secondary creep parts such as stainless steel. The properties of the resulting stress- strain integral are discussed in relation to the direct-superposition method. Finally, example analyses are given. (auth)

Summary (2 min read)

DISCLAIMER

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  • Images are produced from the best available original document. .
  • Metal structures under elevated temperatures undergo significant creep and plastic deformations which generally occur simultaneously.
  • In order to make useful quantitative analysis of current design problems one has to rely on existing material data which are generally limited to the time-dependent behavior of simple structures.
  • Therefore many of the current analytical methods are mere generalizations of existing experimental data rather than fundamental models of material behavior.

GEAP-10546

  • The basic problem lies in generalizing the results of the single-step simple bar experiment to three-dimensional variable stress states.
  • Using a viscoelastic-plastic model, Crochet 19 presented a general solution for a hollow cylinder under internal pressure and a solid cylinder under torsion.
  • Then the incremental stress-strain relations for the combined creep and plasticity problem are derived for both creep theories.
  • The incremental creep strains defined by equation ( 23) if the equation-of-state formulation is selected, in which case the integral in equation (28) is dropped.
  • Iis equation the subscript, n, refers to current time, tn and the prime superscript refers to the derivative with respect to t at tn-The integral terms of the series in equation (30) can be evaluated using any suitable integration algorithim, also known as In tl.

2. UNIAXIAL STRESS-STRAIN LAW

  • The analytical problem may be formulated on the basis of the well known hardening theories of which the strain hardening equation of state theory has been most widely applied.
  • The formulation of this theory is well known and the relevant equations are given without derivation in a later section ..

r=-oo

  • This functional relation can be closely approximated by the following series: e(t) -oo -oo -oo EQUATION Equation (71 is the counterpart of the time-hardening (or strain-hardening) equation in the equation-of-state creep theory.
  • In a creep experiment where the stress o does not vary with time, equation (71 rt'!duces to- (8) which is a polynominal representation of a single-step creep test.
  • In order to make use of this general concept, however, within the limitation of single-step creep data, equation (7) is replaced by the following nonlinear superposition equation: EQUATION where C (o, t) = usual single-step creep formula.
  • It has the advantage, however, of requiring the same creep test as the equation of state theory.

3. • INCREMENTAL .STRESS-STRAIN RELATIONS

  • It remains to derive the creep strain-stress relations.
  • As was mentioned earlier the equation-of-state hardening theory is fairly well known and is fashioned after the plasticity theory.
  • Therefore the basic assumptions stated above have similar implications leading to the following relationship:.

ELASTIC-PLASTIC INCREMENTAL STRESS-STRAIN RELATIONS

  • The instantaneous incremental strain deij is the sum of the elastic strain deij and the plastic strain de~, namely- (1+v) (1-2v) x.
  • From the above, the incremental plastic strain vector must be normal to the loading surface, therefore-.

OUd

  • The free parameter 71. remains to be determined.
  • (A-8) (A-9) Consider a material elemerit'subje.cted to a stress 'state, aij which iies on the yield surface;.
  • The authors restrict attention to stainless steel which is the prime material for liquid metal fast breeder reactors.
  • Differentiating this equation with respect to the stress gives an expression for the creep compliance, namely- where the prime indicates derivative with respect to stress.
  • Following similar argument as before, equation ( B-18) can be written as-.

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GEAP-10546
AEC RESEARCH AND
DEVELOPMENT REPORT
JANUARY
1972
PART
I,
THEORY
REPORT
FOR
CREEP-PLAST
COMPUTER
PROGRAM:
ANALYSIS
OF
TWO-DIMENSIONAL
PROBLEMS
UNDER
SIMULTANEOUS
CREEP
ANO
PLASTICITY
Y.
R.
RASHID
PREPARED FOR UNION CARBIDE CORPORATION
NUCLEAR
DIVISION
SUBCONTRACT NO.
3511
CONTRACT NO.
W7405-ENG.-26
GENERALfj
ELECTRIC
Vt\~
I
(.
t{

DISCLAIMER
This report was prepared as an
account
of
work
sponsored
by
an
agency
of
the United States Government. Neither the United States
Government
nor
any
agency Thereof,
nor
any
of
their
employees,
makes
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warranty, express
or
implied,
or
assumes
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legal
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or
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for
the accuracy, completeness,
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Government
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thereof.

DISCLAIMER
Portions
of
this
document
may
be
illegible
in
electronic
image
products.
Images
are
produced
from
the
best
available
original
document.

29/135-DE
GJw-sn2
r-------N
0
TICE-------
This
report
was
prepared
as
an
account
of
work
sponso~ed
by
the
United
States
Government.
Neither
the
Un.'t~d
States
nor
the
United
States
Atomic
Energy
Co~m1ss1on,
nor
any
of
their
employees,
nor
any
of
theu
contractors,
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their
employees,
makes
_anr.
warranty,
expre5s
or
imµJieJ,
or
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or
responsibility
for
the
accuracy,
com-
pleteness
or
usefulness
of
any
information
apparatus
product
or
process
disclosed,
or
represents'
that
its
us~
would
not
infringe
privately
owned
right.~.
PART I
THEORY REPORT
FOR
CREEP-PLAST
COMPUTER PROGRAM:
ANALYSIS
OF
TWO-DIMENSIONAL PROBLEMS
UNDER SIMULTANEOUS
CREEP
AND
PLASTICITY
Y.
R.
Rashid
Approved:
(l/
W~.
~-Wood,
Manager
Fuel & Material Evaluation
Prepared
for
Union Carbide
Corporation
Nuclear Division
Subcontract
No. 3511
Contract
No. W7405-eng-26
"
..:.~
NUt;U:AH
..
UEL
DEPARTMENT e
GENERAL
ELECTRIC COMPANY
SAN JOSE,
CALIFORNIA
95114
GENERAL.
ELECTRIC
GEAP-10546
AEC Research and
Development
Report
January
1972
O!STRIBUTION
OF
Tli!S
DOCUO:ENT
iS
UNLIW~

LN-1
15/71)
NOTICE
This
report
was prep_ared .as an
account
of
work
sponsored by the- United States
Government. Neither
the
United_ States,nor
the
U_nited
States Atomic Energy Com-
mission, nor any
of
their employees,. nor
any
of their- contractors, subcontractors,
or their
employees. makes
any
warranty, express
or
implied,
or
assumes any legal
liability
or
responsibility for
the
accuracy, completeness
or
usefulness
of
any
information, apparatus.
product
or
process disclosed,
or
represents
that
its use
would
not
infringe privately
owned
rights.
•'·'

Citations
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Journal ArticleDOI
TL;DR: In this article, a strategy for solving problems involving simultaneously occurring large deflections, elastic-plastic material behaviour, and primary creep is described, which involves a double iteration loop at each load level or time.
Abstract: SUMMARY A strategy for solving problems involving simultaneously occurring large deflections, elastic-plastic material behaviour, and primary creep is described. The incremental procedure involves a double iteration loop at each load level or time. In the inner loop the material properties are held constant and the non-linear equilibrium equations are solved by the Newton-Raphson method. These equations are formulated in terms of the tangent stiffness. In the outer loop the plastic and creep strains are determined and the tangent stiffness properties are updated with use of a subincremental algorithm. The magnitude of each time subincrement is determined such that the change in effective stress is less than a preset percentage of the effective stress. The strategy is implemented in a computer pogram, BOSOR 5, for the analysis of shells of revolution. Examples are given of elastic-plastic deformations of a centrally loaded flat plate and elastic-plastic-creep deformations of a beam in bending. The major benefits of the subincremental technique are the increased reliability with which problems involving non-linear plastic and timedependent material behaviour can be solved and the greatly relaxed requirement on the number of load or time increments needed for satisfactory results.

69 citations

Journal ArticleDOI
TL;DR: In this article, a review of currently available incremental theories of plasticity and creep constituitive models is given, and a formulation is presented for the non-isothermal, elastic-plastic-creep-large strain analysis by the finite element method.

7 citations