Probabilistic Simulation of Shape Instability Based on the True Microstructure Model
Shape instability belongs to one of significant types of violation for disposable structural elements under high-stress levels. Due to lack of fundamental data on materials, it is quite problematic to consider the shape instability in the design of disposable structural elements. The crystal plastic...
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Wu, G.C. Li, Y.F. Wang, G.L. 2020-12-21T18:08:13Z 2020-12-21T18:08:13Z 2018 Probabilistic Simulation of Shape Instability Based on the True Microstructure Model / G.C. Wu, Y.F. Li, G.L. Wang // Проблемы прочности. — 2018. — № 1. — С. 56-63. — Бібліогр.: 19 назв. — англ. 0556-171X https://nasplib.isofts.kiev.ua/handle/123456789/173813 539.4 Shape instability belongs to one of significant types of violation for disposable structural elements under high-stress levels. Due to lack of fundamental data on materials, it is quite problematic to consider the shape instability in the design of disposable structural elements. The crystal plastic finite element method is proposed to investigate the dispersion of shape instability life data. It allows these data to be obtained from traditional material parameters. The shape instability behavior is described with the constitutive crystal model of plastic damage accumulation. Then, to improve the accuracy of life prediction, the new method is developed to construct the simulation model of true microstructure. A modeling algorithm based on the image processing technology is provided to reduce the virtual stresses from the transient crystal plastic modeling method. Comparison of experimental and predicted results shows good agreement at high stresses close to the elastic limit of the material. Одним из видов потери устойчивости является формоизменение элементов конструкции одноразового применения при высоких уровнях напряжений. Отсутствие основных данных о материалах не позволяет учесть этот параметр при их проектировании. Предложен метод конечных элементов в пластической постановке для оценки разброса данных о сроке службы элемента при его формоизменении. Для этого могут быть использованы традиционные параметры материала. Характер формоизменения описывается с помощью определяющей модели накопления пластических повреждений на кристалле. Разработан новый метод построения имитационной модели реальной микроструктуры с целью повышения точности прогнозирования срока службы. Моделирующий алгоритм, основанный на технологии обработки изображения, позволяет уменьшить эффект виртуальных напряжений при применении нестационарного метода пластического моделирования на кристалле. Сравнение экспериментальных и расчетных данных демонстрирует их хорошее соответствие при высоких напряжениях, близких к пределу упругости материала. National Natural Science Foundation of China (51405101), the research and innovation fund of Harbin Institute of Technology (Grant Number HIT.NSRIF.2015 053), the China Postdoctoral Science Foundation (Grant Numbers 2014M561340 and 2016T90277) and Heilongjiang Postdoctoral Fund (Grant Number LBH-Z14100). en Інститут проблем міцності ім. Г.С. Писаренко НАН України Проблемы прочности Научно-технический раздел Probabilistic Simulation of Shape Instability Based on the True Microstructure Model Вероятностное моделирование формоизменения на основе модели реальной микроструктуры Article published earlier |
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| title |
Probabilistic Simulation of Shape Instability Based on the True Microstructure Model |
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Probabilistic Simulation of Shape Instability Based on the True Microstructure Model Wu, G.C. Li, Y.F. Wang, G.L. Научно-технический раздел |
| title_short |
Probabilistic Simulation of Shape Instability Based on the True Microstructure Model |
| title_full |
Probabilistic Simulation of Shape Instability Based on the True Microstructure Model |
| title_fullStr |
Probabilistic Simulation of Shape Instability Based on the True Microstructure Model |
| title_full_unstemmed |
Probabilistic Simulation of Shape Instability Based on the True Microstructure Model |
| title_sort |
probabilistic simulation of shape instability based on the true microstructure model |
| author |
Wu, G.C. Li, Y.F. Wang, G.L. |
| author_facet |
Wu, G.C. Li, Y.F. Wang, G.L. |
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Научно-технический раздел |
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Научно-технический раздел |
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2018 |
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English |
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Проблемы прочности |
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Інститут проблем міцності ім. Г.С. Писаренко НАН України |
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Article |
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Вероятностное моделирование формоизменения на основе модели реальной микроструктуры |
| description |
Shape instability belongs to one of significant types of violation for disposable structural elements under high-stress levels. Due to lack of fundamental data on materials, it is quite problematic to consider the shape instability in the design of disposable structural elements. The crystal plastic finite element method is proposed to investigate the dispersion of shape instability life data. It allows these data to be obtained from traditional material parameters. The shape instability behavior is described with the constitutive crystal model of plastic damage accumulation. Then, to improve the accuracy of life prediction, the new method is developed to construct the simulation model of true microstructure. A modeling algorithm based on the image processing technology is provided to reduce the virtual stresses from the transient crystal plastic modeling method. Comparison of experimental and predicted results shows good agreement at high stresses close to the elastic limit of the material.
Одним из видов потери устойчивости является формоизменение элементов конструкции одноразового применения при высоких уровнях напряжений. Отсутствие основных данных о материалах не позволяет учесть этот параметр при их проектировании. Предложен метод конечных элементов в пластической постановке для оценки разброса данных о сроке службы элемента при его формоизменении. Для этого могут быть использованы традиционные параметры материала. Характер формоизменения описывается с помощью определяющей модели накопления пластических повреждений на кристалле. Разработан новый метод построения имитационной модели реальной микроструктуры с целью повышения точности прогнозирования срока службы. Моделирующий алгоритм, основанный на технологии обработки изображения, позволяет уменьшить эффект виртуальных напряжений при применении нестационарного метода пластического моделирования на кристалле. Сравнение экспериментальных и расчетных данных демонстрирует их хорошее соответствие при высоких напряжениях, близких к пределу упругости материала.
|
| issn |
0556-171X |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/173813 |
| citation_txt |
Probabilistic Simulation of Shape Instability Based on the True Microstructure Model / G.C. Wu, Y.F. Li, G.L. Wang // Проблемы прочности. — 2018. — № 1. — С. 56-63. — Бібліогр.: 19 назв. — англ. |
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| fulltext |
UDC 539.4
Probabilistic Simulation of Shape Instability Based on the True Microstructure
Model
G. C. Wu, Y. F. Li,
1
and G. L. Wang
School of Mechanical Engineering, Harbin Institute of Technology, Harbin, China
1 yuefengli@hit.edu.cn
Shape instability belongs to one of significant types of violation for disposable structural elements
under high-stress levels. Due to lack of fundamental data on materials, it is quite problematic to
consider the shape instability in the design of disposable structural elements. The crystal plastic finite
element method is proposed to investigate the dispersion of shape instability life data. It allows these
data to be obtained from traditional material parameters. The shape instability behavior is described
with the constitutive crystal model of plastic damage accumulation. Then, to improve the accuracy of
life prediction, the new method is developed to construct the simulation model of true microstructure.
A modeling algorithm based on the image processing technology is provided to reduce the virtual
stresses from the transient crystal plastic modeling method. Comparison of experimental and predicted
results shows good agreement at high stresses close to the elastic limit of the material.
Keywords: shape instability failure, low-cycle fatigue, true microstructure, finite element
analysis, disposable structural elements.
Introduction. Shape instability behavior has been commonly investigated as a special
type of ratcheting, which mainly refers to the elastic-plastic dynamic transition process of
materials. Shape instability is critical for disposable structural elements which are specially
designed to undertake high overload cyclic stresses [1]. Therefore, the shape instability is
identified via cyclic stress–strain curves as the state with 0.2% total plastic strain. In order
to estimate the reliability of disposable structural elements, it is necessary to obtain the
shape instability life scatter. Large scale tests are required. Moreover, as shape instability
behavior only concerns the beginning stage of plastic deformation, the failure data have to
be picked up from the cyclic stress–strain tests curves. The whole process is inefficient.
Therefore, it is necessary to use a new efficient method to predict the shape instability
failure.
Shape instability behavior is the result of multi plastic behavior of materials, such as
low cycle fatigue damage, cyclic softening and ratcheting behavior [2–6]. Generally, the
traditional crystal plastic model ignores the inhomogeneity of material properties at the
microlevel [7–9]. It means that these models lack the ability to predict failure, depending on
the main control factors of shape instability behavior. Therefore, in order to involve the
material behavior mentioned above in the simulation model, a proper life prediction method
based on the true microstructure model is developed for the shape instability failure
prediction, which will provide a more accurate description on fatigue plastic deformation
during the elastic–plastic transition. By choosing material parameters reasonably, probability
crystal plastic finite element method is proved to be a wonderful way to investigate the
dispersion of shape instability life. However, due to the differences between the true
microstructure and simulated models, the simulation can hardly provide accurate
distribution features, because the available method used in the simulation model is not
accurate enough to simulate the complexity of microstructure. Therefore, in this study, a
modeling algorithm based on the image processing technology is provided to solve this
problem.
© G. C. WU, Y. F. LI, G. L. WANG, 2018
56 ISSN 0556-171X. Ïðîáëåìè ì³öíîñò³, 2018, ¹ 1
1. Experimental Procedure and Modeling Method. Firstly, quenched and tempered
40Cr steel, which is a typical material used in the transmission elements, was chosen for
this study. After quenching and tempering treatment, the hardness of hot-rolled 40Cr steel
bars was about HRC = 28–30. The gauge diameter and length of specimens is machined
into 12 and 25 mm, respectively. After successively turning and polishing processes, the
surface scratches of specimens could be removed.
Then, full tension–compression tests are conducted to identify material fatigue
damage parameters in simulation models. Shape instability behavior tests are conducted to
compare with the numerical model. Mean stress and stress amplitude are more frequently
used in fatigue investigations, but not common parameters in the mechanical design.
Therefore, adapt to mechanical design requirements, the maximum stress and stress ratio,
calculated according to the maximum load and fatigue feature, are used as the control
parameters in the tests.
Finally, to predict shape instability failure, a simulation model is established by using
a proper material constitutive model, especially for the initial stage of fatigue process. The
constitutive model will be present in Section 3. A geometric model similar to the true
microstructure is also significant to reflect the microcyclic plastic strain and ratcheting
strain. Therefore, this study proposed a method to build numerical models in the commercial
finite element analysis software ABAQUS. As shown in Fig. 1, firstly, the true microstructure
of steel 40Cr is obtained by using electron backscatter diffraction measurements. Then, the
grain boundary could be preliminary identified based on the image processing technology.
By doing this, the chromatic image is transformed to a new gray-scale image. Actually, the
crystal orientation information is abandoned in this process, because it is not necessary to
accurately copy the crystal orientation in the numerical model. At this time, the grain
boundaries are not clear enough to exact single grains. Therefore, a denoising process is
essential to delete unreasonable lines. A unique requirement in this stage is that the lines
forming grains should be closed; otherwise, the open lines will bring mistakes in the grains
geometry model restructure process. Finally, the independent grains with clear boundaries
are exacted. The topography information could be output as the required format of input
file by ABAQUS. The geometry model is similar with the true microstructure of materials.
After determining the model scale, the performances of grains in the model, including
the elastic module and the yield strength of the grains, are directly obtained via nano-
indentation tests or indirectly determined from stress–strain curve referring to the method
provided by Liu and Chen [10]. Figure 2 shows the fifty random position points used to
conduct the tests on the specimen. According to these material data, Gaussian distribution
parameters could be fitted. For the steel 40Cr specimens in this study, the elastic limit had
an expected value 790 MPa and standard deviation 92 MPa, respectively.
2. Simulation. For the purpose of predicting the shape instability failure, it is essential
to investigate shape instability behavior and estimate shape instability life by using a proper
model based on damage-coupled cyclic plasticity theory. According to the determination
rule of shape instability failure, 0.2% total plastic strain occurs in the initial stage of the
fatigue process, which contains cyclic plastic strain and ratcheting strain. Therefore, the
cyclic plastic behavior of metallic materials is described based on the frame of Frederick–
Armstrong model [11]. The evolution law supposed by Ohno and Wang is used to avoid the
overestimation of ratcheting strain in the initial stage of cyclic plastic behavior [12, 13].
The elastic–plastic fatigue damage model has been provided by Lemaitre and Chaboche
[14]. By utilizing the UMAT function offered in the software ABAQUS, damaged-coupled
cyclic crystal plastic constitutive numerical equations was programmed, which was given in
our previous work [15, 16]. The main control equations are simply presented as followed:
The total strain � ij is as follows:
� � �ij ij
e
ij
p� � . (1)
Probabilistic Simulation of Shape Instability ...
ISSN 0556-171X. Ïðîáëåìè ì³öíîñò³, 2018, ¹ 1 57
The elastic strain, � ij
e , is expressed as
�
� � � � �
ij
e ij kk ij
E D E D
�
�
�
��
�
���
�
��
�
��
1
1 1
, (2)
where � is Poisson’s ratio, E is elastic modulus, � ij is Cauchy stress tensor, D is
damage parameter, � kk is the main diagonal component of � ij , and � ij are Kronecker
delta.
G. C. Wu, Y. F. Li, and G. L. Wang
58 ISSN 0556-171X. Ïðîáëåìè ì³öíîñò³, 2018, ¹ 1
a b
dc
Fig. 1. The procedure to build a geometric model according to EBSD test figure: (a) EBSD figure;
(b) grain boundary initial identification; (c) grain boundary processing; (d) grain exaction and
topological information output.
Fig. 2. Nano-indentation test conducted at 50 random points to obtain grain mechanics performances.
The evolution law of plastic strain, �ij
p
, is expressed as
� �
�
��ij
p
ij
F
� , (3)
where � is a non-negative scalar.
The Mises yield function with damage F is given as follows:
F
D
a
D
a Q
dev dev�
�
�
�
�
�
�
�
�
�
�
��
�
�� �
3
2 1 1
1 2
� �
: ,
/
(4)
where � dev is the deviatoric stress tensor and a is the backstress tensor in deviatoric
space.
The yield surface Q is expressed as
Q p Q Q b� ��( ) ,1 (5)
where Q� and b1 are material constants, p is given as
p
Dij
p
ij
p�
�
�
� �
�
2
3 1
1 2
( : ) .
/
� �
�
(6)
The back stress tensor a in the Eq. (4) is expressed as
a a i
i
m
�
�
� ( )
1
( , , ... , ),i n� 1 2 (7)
where m is the backstress component number, a i( ) is given as
a D c r
r
ai i i p
i
i
n
p
i
( ) ( ) ( )
( )
( )
(
( )
| | | |
:� � �
�
�
�
�
�1
2
3
�
�
�
)
( )
( )
| | | |
,
a
a
i
i
�
�
�
�
�
�
�
�
(8)
| | | | : ,( ) ( ) ( )a a ai i i� (9)
where c i( ) , r i( ) , and n are material constants.
The damage parameter, D, is expressed as follows:
�
� �
� �
�
D
N
D
A
M b D
II
mean
� � �
� �
��
�
��
�[ ( ) ]
( )( )
,1 1
1 3 1
1
0 2
(10)
where �, �, M 0, and b2 are material constants, � mean is the mean value belonging to
hydrostatic stress, which is zero, and AII is the parameter determined by the Sines yield
criterion.
On the basis of the shape instability life character, the heterogeneity of materials needs
to be considered in the prediction of shape instability failure. The heterogeneity of a
material mainly includes two aspects, the microstructure features and the grain mechanics
ISSN 0556-171X. Ïðîáëåìè ì³öíîñò³, 2018, ¹ 1 59
Probabilistic Simulation of Shape Instability ...
properties. Therefore, a two-dimensional probabilistic crystal cyclic plastic finite element
model is built to predict shape instability failure.
Figure 3 shows the process to copy the true microstructural and grain performances in
the simulation model to predict the shape instability failure prediction in ABAQUS. As
shown in Fig. 3a, representative elementary volume (RVE) with different stochastic micro-
structures are established in ABAQUS. Figure 3b shows the method to assign random
material performances in the RVE model. Based on the obtained Gaussian distribution in
Section 2, mechanics properties are randomly produced, applying to assign to the grains in
RVE. After endowing the elements with the fatigue damage-coupled cyclic plastic material
constitutive model, the simulation model could present mechanics properties with the true
specimens on the microlevel. As the morphology and the grain properties of RVE are both
randomly generated, the failure could be simulated by using different random numbers. The
simulation results will reflect the material mechanical property dispersion on a macrolevel,
which is accordance with the practical situation.
60 ISSN 0556-171X. Ïðîáëåìè ì³öíîñò³, 2018, ¹ 1
G. C. Wu, Y. F. Li, and G. L. Wang
a
b
Fig. 3. Schematic showing the method used to simulate the probabilistic failures of shape instability
behavior: (a) the simulation model selected from any part of the whole model; (b) the stochastic
performances of grains based Monte-Carlo method.
3. Results and Discussion. Generally, the influence level of artificial stresses in the
simulation model is difficult to evaluate, because they are coupled with many other factors.
Therefore, the model based on the Voronoi tessellation is usually established based on the
uniform distribution to avoid artificial stresses. However, it will ignore the complexity of
microstructure. The new modeling method could obviously decrease the differences
between simulation models and true microstructure. By doing this, the problem to evaluate
artificial stresses is technically bypassed and then solved.
Figure 4 compares the simulated life scatter with the experiment results. The
stress–strain curves with 0.2% total plastic strain are picked out from these hysteresis
curves obtained from the experiments or the simulations. It can be seen that the required
number of cycles needed to reach 0.2% plastic strain is different between the experiments
and the simulations. The differences are a result of the stochastic simulation procedure. To
obtain the life scatter band, a group of material properties is randomly generated based on a
certain distribution. These material properties are also randomly assigned in the simulation
model elements. The overall performance of the simulation models vary with each
simulation. These variations yield the life scatter, but they also lead to differences between
the simulation and the experimental results in one certain simulation calculation. If the
stochastic procedure is removed from the simulation model, then results identical to the
experimental data can be obtained by using suitable material parameters; the constitutive
models used in this paper have been validated in many studies [17–19]. As the figure
shows, the prediction model is more accurate at high-stress levels than a low-stress levels,
especially at 0.95� s . Errors occur between the simulation and the experiment when the
maximum stress was at 0.7� s . The errors come from the damage parameter, D, used in the
constitutive model. Steel 40Cr presents high cycle fatigue features at 0.7� s maximum
stress. However, D is determined based on the assumption of low-cycle fatigue statuses,
which means that larger D values are used in the constitutive model. Therefore, the
simulation shape instability life is shorter than that determine experimentally. Although the
errors are at low-stress levels, the simulation method provides accurate prediction results
for shape instability life at high-stress levels, which is more significant for applications in
disposable structural elements design. Therefore, the deviation could be ignored when it is
at low-stress levels.
Conclusions. Disposable structural elements are rarely mentioned but widely applied
in aerospace vehicles. Based on the high payload requirements, disposable structural
elements usually undertake higher stress levels than general structural elements. Under
these circumstances, shape instability failure is significantly increased. Therefore, this
study provides a numerical simulation method based on the true microstructure model for
the shape instability failure. A modeling method based on the image processing technology
ISSN 0556-171X. Ïðîáëåìè ì³öíîñò³, 2018, ¹ 1 61
Probabilistic Simulation of Shape Instability ...
Fig. 4. Comparison between the experiment and the simulated results of 40Cr steel life predictions.
is developed to simulate the true microstructure. The comparison between the experiments
and predictions shows good agreement in the concerned process. By doing this, the
numbers of shape instability life tests could be significantly decreased.
Acknowledgments. National Natural Science Foundation of China (51405101), the
research and innovation fund of Harbin Institute of Technology (Grant Number
HIT.NSRIF.2015 053), the China Postdoctoral Science Foundation (Grant Numbers
2014M561340 and 2016T90277) and Heilongjiang Postdoctoral Fund (Grant Number
LBH-Z14100).
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Received 15. 09. 2017
ISSN 0556-171X. Ïðîáëåìè ì³öíîñò³, 2018, ¹ 1 63
Probabilistic Simulation of Shape Instability ...
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/ENU (Use these settings to create Adobe PDF documents best suited for high-quality prepress printing. Created PDF documents can be opened with Acrobat and Adobe Reader 5.0 and later.)
>>
/Namespace [
(Adobe)
(Common)
(1.0)
]
/OtherNamespaces [
<<
/AsReaderSpreads false
/CropImagesToFrames true
/ErrorControl /WarnAndContinue
/FlattenerIgnoreSpreadOverrides false
/IncludeGuidesGrids false
/IncludeNonPrinting false
/IncludeSlug false
/Namespace [
(Adobe)
(InDesign)
(4.0)
]
/OmitPlacedBitmaps false
/OmitPlacedEPS false
/OmitPlacedPDF false
/SimulateOverprint /Legacy
>>
<<
/AddBleedMarks false
/AddColorBars false
/AddCropMarks false
/AddPageInfo false
/AddRegMarks false
/ConvertColors /ConvertToCMYK
/DestinationProfileName ()
/DestinationProfileSelector /DocumentCMYK
/Downsample16BitImages true
/FlattenerPreset <<
/PresetSelector /MediumResolution
>>
/FormElements false
/GenerateStructure false
/IncludeBookmarks false
/IncludeHyperlinks false
/IncludeInteractive false
/IncludeLayers false
/IncludeProfiles false
/MultimediaHandling /UseObjectSettings
/Namespace [
(Adobe)
(CreativeSuite)
(2.0)
]
/PDFXOutputIntentProfileSelector /DocumentCMYK
/PreserveEditing true
/UntaggedCMYKHandling /LeaveUntagged
/UntaggedRGBHandling /UseDocumentProfile
/UseDocumentBleed false
>>
]
>> setdistillerparams
<<
/HWResolution [2400 2400]
/PageSize [612.000 792.000]
>> setpagedevice
|