Micromechanical Coupled Study of Crack Growth Initiation Criterion in Pressure Vessel Steel
We present results of the combined design-theoretical investigation of the mechanism of crack growth at the onset of ductile fracture of NPP reactor pressure vessels. Micromechanical approach to the prediction of ductile fracture has been applied, according to which the volume fraction of voids...
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Інститут проблем міцності ім. Г.С. Писаренко НАН України
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Rakin, M. Sedmak, A. Cvijovic, Z. Zrilic, M. Sedmak, S. 2013-07-09T13:31:30Z 2013-07-09T13:31:30Z 2004 Micromechanical Coupled Study of Crack Growth Initiation Criterion in Pressure Vessel Steel / M. Rakin, A. Sedmak, Z. Cvijovic, M. Zrilic, S. Sedmaka // Проблемы прочности. — 2004. — № 1. — С. 48-53. — Бібліогр.: 12 назв. — англ. 0556-171X https://nasplib.isofts.kiev.ua/handle/123456789/47060 539.4 We present results of the combined design-theoretical investigation of the mechanism of crack growth at the onset of ductile fracture of NPP reactor pressure vessels. Micromechanical approach to the prediction of ductile fracture has been applied, according to which the volume fraction of voids in the deformed material is determined by finite-element method. On the basis of CT-specimen tests and known damage parameters, obtained on smooth spherical specimens, we obtained micromechanical criterion of crack growth initiation for ductile fracture. Представлены результаты комплексного расчетно-экспериментального исследования механизма распространения трещины на начальном этапе вязкого разрушения корпусных сталей АЭС. Использован микромеханический подход к прогнозированию вязкого разрушения, согласно которому объемное содержание пор деформируемого материала определяется методом конечных элементов. На основании проведенных испытаний образцов СТ с трещиной и имеющихся данных о параметрах разрушения гладких сферических образцов установлен микромеханический критерий начала развития трещины в условиях вязкого разрушения материала. Представлено результати комплексного розрахунково-експериментального дослідження механізму розповсюдження тріщини на початковому етапі в’язкого руйнування корпусних сталей АЕС. Використовується мікромеха- нічний підхід до прогнозування в ’язкого руйнування, згідно з яким об’ємний вміст пор деформівного матеріалу визначається методом скінченних елементів. На основі проведених випробувань зразків СТ із тріщиною та відомих даних про параметри руйнування гладких сферичних зразків установлено мікромеханічний критерій початку розвитку тріщини в умовах в ’язкого руйнування. en Інститут проблем міцності ім. Г.С. Писаренко НАН України Проблемы прочности Научно-технический раздел Micromechanical Coupled Study of Crack Growth Initiation Criterion in Pressure Vessel Steel Комплексное микромеханическое исследование на основе критерия инициации трещины при вязком разрушении корпусных сталей Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
| title |
Micromechanical Coupled Study of Crack Growth Initiation Criterion in Pressure Vessel Steel |
| spellingShingle |
Micromechanical Coupled Study of Crack Growth Initiation Criterion in Pressure Vessel Steel Rakin, M. Sedmak, A. Cvijovic, Z. Zrilic, M. Sedmak, S. Научно-технический раздел |
| title_short |
Micromechanical Coupled Study of Crack Growth Initiation Criterion in Pressure Vessel Steel |
| title_full |
Micromechanical Coupled Study of Crack Growth Initiation Criterion in Pressure Vessel Steel |
| title_fullStr |
Micromechanical Coupled Study of Crack Growth Initiation Criterion in Pressure Vessel Steel |
| title_full_unstemmed |
Micromechanical Coupled Study of Crack Growth Initiation Criterion in Pressure Vessel Steel |
| title_sort |
micromechanical coupled study of crack growth initiation criterion in pressure vessel steel |
| author |
Rakin, M. Sedmak, A. Cvijovic, Z. Zrilic, M. Sedmak, S. |
| author_facet |
Rakin, M. Sedmak, A. Cvijovic, Z. Zrilic, M. Sedmak, S. |
| topic |
Научно-технический раздел |
| topic_facet |
Научно-технический раздел |
| publishDate |
2004 |
| language |
English |
| container_title |
Проблемы прочности |
| publisher |
Інститут проблем міцності ім. Г.С. Писаренко НАН України |
| format |
Article |
| title_alt |
Комплексное микромеханическое исследование на основе критерия инициации трещины при вязком разрушении корпусных сталей |
| description |
We present results of the combined design-theoretical
investigation of the mechanism of crack
growth at the onset of ductile fracture of NPP reactor
pressure vessels. Micromechanical approach to
the prediction of ductile fracture has been applied,
according to which the volume fraction of voids in
the deformed material is determined by finite-element
method. On the basis of CT-specimen tests
and known damage parameters, obtained on
smooth spherical specimens, we obtained
micromechanical criterion of crack growth initiation
for ductile fracture.
Представлены результаты комплексного расчетно-экспериментального исследования механизма
распространения трещины на начальном этапе вязкого разрушения корпусных сталей
АЭС. Использован микромеханический подход к прогнозированию вязкого разрушения,
согласно которому объемное содержание пор деформируемого материала определяется
методом конечных элементов. На основании проведенных испытаний образцов СТ с трещиной
и имеющихся данных о параметрах разрушения гладких сферических образцов установлен
микромеханический критерий начала развития трещины в условиях вязкого разрушения
материала.
Представлено результати комплексного розрахунково-експериментального
дослідження механізму розповсюдження тріщини на початковому етапі
в’язкого руйнування корпусних сталей АЕС. Використовується мікромеха-
нічний підхід до прогнозування в ’язкого руйнування, згідно з яким об’ємний
вміст пор деформівного матеріалу визначається методом скінченних елементів.
На основі проведених випробувань зразків СТ із тріщиною та відомих
даних про параметри руйнування гладких сферичних зразків установлено
мікромеханічний критерій початку розвитку тріщини в умовах в ’язкого
руйнування.
|
| issn |
0556-171X |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/47060 |
| citation_txt |
Micromechanical Coupled Study of Crack Growth Initiation Criterion in Pressure Vessel Steel / M. Rakin, A. Sedmak, Z. Cvijovic, M. Zrilic, S. Sedmaka // Проблемы прочности. — 2004. — № 1. — С. 48-53. — Бібліогр.: 12 назв. — англ. |
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| first_indexed |
2025-11-26T14:59:56Z |
| last_indexed |
2025-11-26T14:59:56Z |
| _version_ |
1850627232419020800 |
| fulltext |
UDC 539.4
Micromechanical Coupled Study of Crack Growth Initiation Criterion
in Pressure Vessel Steel
M. Rakin,a A. Sedm ak,b Z. Cvijovic,a M. Zrilic,a and S. Sedm aka
a Belgrade University, Faculty of Technology and Metallurgy, Belgrade, Serbia and
Montenegro
b Belgrade University, Faculty of Mechanical Engineering, Belgrade, Serbia and
Montenegro
УДК 539.4
Комплексное микромеханическое исследование на основе
критерия инициации трещины при вязком разрушении
корпусных сталей
М. Ракина, А. Седмак6, 3. Ц вийовича, М. Зрилича, С. Седмака
а Белградский университет, факультет технологии и металлургии, Белград, Сербия и
Черногория
б Белградский университет, факультет машиностроения, Белград, Сербия и Черногория
Представлены результаты комплексного расчетно-экспериментального исследования меха
низма распространения трещины на начальном этапе вязкого разрушения корпусных сталей
АЭС. Использован микромеханический подход к прогнозированию вязкого разрушения,
согласно которому объемное содержание пор деформируемого материала определяется
методом конечных элементов. На основании проведенных испытаний образцов СТ с тре
щиной и имеющихся данных о параметрах разрушения гладких сферических образцов уста
новлен микромеханический критерий начала развития трещины в условиях вязкого разру
шения материала.
Ключевые слова : комплексное микромеханическое моделирование, доля
объемных пустот, метод конечных элементов, критерий развития трещины.
Introduction. Micromechanism of ductile fracture of most metals and alloys
includes void nucleation, growth and coalescence. In steels, voids nucleate at
non-metallic inclusions and second-phase particles. Micromechanical approach to
fracture mechanics has been introduced in an effort to describe the process of
fracture in a way that is as close to the actual phenomena in a material as possible.
Such an approach is based on the models that account for and quantify the
process of microscopic damages, in order to predict macroscopic failure.
Micromechanical approach to the analysis of ductile fracture requires
combined experimental and numerical procedure. According to the uncoupled
micromechanical damage models, the damage parameter is calculated in
postprocessing phase of the finite element (FE) analysis. In the coupled
micromechanical models, one or more damage parameters are calculated to
© M. RAKIN, A. SEDMAK, Z. CVIJOVIC, M. ZRILIC, S. SEDMAK, 2004
48 ISSN 0556-171X. Проблемы прочности, 2004, № 1
Micromechanical Coupled Study o f .
predict ductile fracture initiation. Thus, the FE analysis must include procedure
for calculation of these parameters and optionally, fracture initiation criterion.
The most frequently used damage parameter is void volume fraction, f .
In present study, we apply micromechanical model based on a particular
yield criterion of a porous solid, proposed by Gurson [1] and later modified by
Tvergaard and Needleman [2, 3] (the GTN model). This model was incorporated
into the software program using FE method. The present research is a
continuation of the Round Robin project [4], aimed at defining the criterion of the
crack growth onset on CT specimens using values of micromechanical parameters
determined on simple round specimens.
M icromechanical Model. Coupled approach to the material damage and
ductile fracture initiation considers alloy as a porous medium where the influence
of nucleated voids on the stress-strain state and plastic flow cannot be avoided.
The GTN model is based on the hypothesis that void nucleation and growth in
metal may be macroscopically described by extending the von Mises plasticity
theory to cover the effects of porosity occurring in the material. Thus the void
volume fraction f as a variable is introduced into expression for plastic potential
[1-3]:
3o 'ij °'ij _ .* j 3 o N
/ ■ + 2 q i f * c o s h e r ] - [1 + (q i f * )2 ] = 0, (1)
where o denotes actual yield stress of the material matrix, o' j is the stress
deviator, while q1 is the constitutive parameter introduced by Tvergaard [2] to
improve the ductile fracture prediction of the Gurson model, and f is a function
of the void volume fraction [3]:
for f ^ f c ,
■f c ) for f > f c , (2)
where f c is the critical value at which void coalescence occurs. Parameter K
defines slope of the sudden drop of the load on the load-diameter reduction
*
diagram and is often referred to as “accelerating factor.” For f = 0, the plastic
potential [Eq. (1)] is identical with that of von Mises.
Initial void volume fraction f o depends on the volume fraction of
non-metallic inclusions in steel, f 'v . Under plastic strain, voids in the material
matrix first nucleate on these non-metallic inclusions. In the final stage of ductile
fracture, the voids may intensively nucleate on the secondary-phase particles (the
so-called secondary voids).
Tested Steel. The low-alloyed pressure-vessel steel of designation
22NiMoCr37 according to the German standard (DIN) has been tested. The
experiments have been carried out on the specimens of steel in forged heat-treated
condition. The steel was produced at Siemens and used in [5].
The chemical composition of steel is given in Table 1.
Major mechanical properties of tested steel are: Rp 0 2 = 476 MPa, R m =
= 620 MPa, and E =203,000 MPa. Optical microscopy of etched specimens has
ISSN 0556-171X. npo6n.eubi npounocmu, 2004, № 1 49
M. Rakin, A. Sedmak, Z. Cvijovic, et al.
shown that tested steel consists of polygonal ferrite and beinite. Using planimetric
method o f measurement on the specimens in polished state according to ASTM
E 1245-89, it has been established that the steel contains non-metallic inclusions
of sulfide and oxide type and a number of complex oxide-sulfide inclusions.
Determined mean value of non-metallic volume fraction is f v = 0.00236.
Average value of mean free path between inclusions is 2 = 243.1 ^m.
T a b l e 1
Chemical Composition of Steel 22NiMoCr37 (in wt.%)
C Si Mn P S Cr Mo Ni Cu Al
0.22 0.21 0.86 0.018 0.011 0.42 0.83 0.92 0.05 0.015
Results and Discussion. The critical value of void volume fraction
f c = 0.00611 has been determined by experimental and numerical procedures of
testing of smooth round specimens. At this value of f c in the center of a smooth
specimen final loss of the material loading capacity occurs, followed by fracture.
Optical and scanning electron microscopy and FE elastic-plastic calculations have
shown that the influence of the secondary-phase particles on the final phase of
ductile fracture of tested steel is low [6, 7]. Therefore it is here assumed that the
initial void volume fraction corresponds to the volume fraction of non-metallic
inclusions, f 0 = f v , while the influence of the secondary-voids nucleation is
neglected.
For determination of the onset of stable crack growth at the beginning of
ductile fracture, the CT25 specimens (B = 25 mm, W = 50 mm) with a 0 / W ~ 0.55
were used. Using the “single specimen method,” force-crack mouth opening
displacement diagram (F — CMOD) and the resistance curve to the crack growth,
J — Aa (Fig. 1) have been determined.
Fig. 1. J — Aa curve and blunting line.
50 ISSN 0556-171X. npo6neMbi npouHocmu, 2004, № 1
Micromechanical Coupled Study o f .
According to the ESIS procedure [8], through the experimental points a
polynomial of third order has been drawn in Fig. 1 that in proper way represents
the curve of resistance. The blunting line has been located according to the mean
value of final stretch zone width AaZR = 91.15 /im determined by measurement
on three broken CT specimens according to [9]. Bisection of the blunting and
polynomial has given the value of /-integral corresponding to the onset of crack
growth: J i = 259 N/mm, according to [8]. The value obtained for J i is rather
high, which indicates a very good resistance to the mechanism of the onset of
ductile fracture for the tested pressure-vessel steel.
One half of the specimen has been numerically modeled using a mesh of
finite elements (FE) in a plane. Eight-node isoparametric FE under conditions of
plane strain is used (Fig. 2). The material non-linearity is modeled by a curve true
stress vs true (logarithmic) strain. Loading is modeled by a large number of
prescribed displacements of a node on the left edge of the mesh (Fig. 2a).
Fig. 2. Finite element mesh for CT25 specimen (a) and crack tip detail (b).
Crack tip is modeled solely by a FE-mesh refinement in the crack zone
(Fig. 2b). It has turned out [10] that the FE-size in front of a crack tip
significantly affects the accuracy of modeling of crack growth initiation. The
question is how to define the FE size at a crack tip and get an actual result at the
beginning of a crack growth for the parameters of fracture mechanics that
quantify the onset of a crack growth: J-integral ( J t) or crack tip opening
displacement, CTOD (d 5i).
It has been shown elsewhere [10] that, in case of application of the reduced
Gauss integration, the FE size in front of the crack tip approximates to an average
value of the mean path X. This result is in accordance with previous research [11,
12]. Therefore the FE size of 0.25 X 0.25 mm in ligament is adopted. The
quadratic FE is used, since no significant influence of test direction on the mean
free path X has been observed [10].
Figure 3 shows diagram F — CMOD up to the moment of the onset of the
crack growth. A very good agreement of experimental and numerically calculated
curves is obtained.
ISSN 0556-171X. npo6n.eubi npounocmu, 2004, N 1 51
M. Rakin, A. Sedmak, Z. Cvijovic, et al.
b
Fig. 3. Diagram F —CMOD (a) and magnification at crack growth initiation point (b).
./-integral corresponding to the onset of the crack growth has been calculated
based on the work of an external force, below the numerically obtained curve,
according to [8]. Failure criterion has been defined by
f > f c , (3)
where f is a void volume fraction determined by elastic-plastic FE
calculations, and f c = 0.00611 is critical void volume fraction. The crack begins
to grow when the criterion given by [3] is satisfied in any of the Gauss points in a
FE nearest to the crack tip. In this way / i = 270.4 N/mm has been calculated,
which is in a very good agreement with the experimental value.
Conclusions. In this research, using coupled micromechanical analysis, the
onset of the crack growth in CT specimens has been successfully foreseen, based
on the critical void volume fraction f c (determined on smooth round specimens)
and mean free path X. Further research envisages modeling of a stable crack
growth.
52 ISSN 0556-171X. npo6n.eubi npounocmu, 2004, № 1
Micromechanical Coupled Study o f .
Р е з ю м е
Представлено результати комплексного розрахунково-експериментального
дослідження механізму розповсюдження тріщини на початковому етапі
в’язкого руйнування корпусних сталей АЕС. Використовується мікромеха-
нічний підхід до прогнозування в ’язкого руйнування, згідно з яким об’ємний
вміст пор деформівного матеріалу визначається методом скінченних елемен
тів. На основі проведених випробувань зразків СТ із тріщиною та відомих
даних про параметри руйнування гладких сферичних зразків установлено
мікромеханічний критерій початку розвитку тріщини в умовах в ’язкого
руйнування.
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growth: Part I. Yield criteria and flow rules for porous ductile media,” J.
Eng. Mater. Techn. 99, 2-15 (1977).
2. V. Tvergaard, “Influence of voids on shear band instabilities under plane
strain conditions,” Int. J. Fract., 17, 389-407 (1981).
3. V. Tvergaard and A. Needleman, “Analysis of cupe-cone fracture in a round
tensile bar,” Acta Met., 32, 157-169 (1984).
4. G. Bernauer and W. Brocks, Numerical Round Robin on Micromechanical
Models - Results, ESIS TC8, Institute for Materials Research, GKSS
Research Center, Geesthacht (2000).
5. J. Heerens and D. Hellmann, Fracture Toughness o f Steel in the Ductile to
Brittle Transition Regime, Final Report of the EU-Project MAT1-CT-940080,
GKSS Research Center, Geesthacht, (1999).
6. M. Rakin, Z. Cvijovic, A. Sedmak, and S. Sedmak, “Analysis of the
transferability of micromechanical parameters of damage of steel under
conditions of ductile-fracture initiation,” Mater. Sci., 38, 104-113 (2002).
7. M. Rakin, Z. Cvijovic, and A. Sedmak, “Study of physical significance of
some micromechanical parameters in ductile fracture analysis,” in: Book of
Abstr. of ESIS TC1 and TC8 Spring Meeting, (Paris, France, 2002), ESIS-
CEA, Paris (2002), p. 13.
8. ESIS Procedure fo r Determining the Fracture Behavior o f Materials,
European Structural Integrity Society, ESIS P2-92 (1992).
9. Ermittlung von Rissinitierungswerten und Risswiderstands-Kurven bei
Anwendung des J-Integrals, DVM 002, Deutscher Verband fcr Material
prüfung (1987).
10. M. Rakin, Z. Cvijovic, V. Grabulov, S. Putic and A. Sedmak, “Prediction of
ductile fracture initiation using micromechanical analysis,” Eng. Fract.
Mech. (in print).
11. D-Z. Sun, R. Kienzler, B. Voss, and W. Schmitt, in: Fracture Mechanics
(Twenty-Second Symp.), Atluri S. N., Newman J. C., Raju Jr. I., and Epstein
J. S. (Eds.), ASTM STP 1131, Vol. II, Philadelphia (1992), pp. 368-378.
12. C. Poussard and C. Sainte Catherine, “CEA Contribution to the ESIS TC8
Round Robin on numerical methods,” Phase II, Task A, ESIS TC8 Meeting,
Swansea (1999).
Received 26. 05. 2003
ISSN 0556-171X. Проблеми прочности, 2004, № 1 53
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