Influence of a Strain Rate and Temperature on the Crack Tip Stress and Microstructure Evolution of Monocrystalline Nickel: a Molecular Dynamics Simulation
The effect of a strain rate and temperature on the crack tip stress and microstructure evolution ahead of a growing crack in monocrystalline nickel are studied by molecular dynamics simulations. The correlation between the microstructure evolution and stress field near the crack tip is also ex...
Saved in:
| Published in: | Проблемы прочности |
|---|---|
| Date: | 2014 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут проблем міцності ім. Г.С. Писаренко НАН України
2014
|
| Subjects: | |
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/112702 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Influence of a Strain Rate and Temperature on the Crack Tip Stress and Microstructure Evolution of Monocrystalline Nickel: a Molecular Dynamics Simulation / W.P. Wua, Z.Z. Yao // Проблемы прочности. — 2014. — № 2. — С. 12-21. — Бібліогр.: 31 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1859738575809019904 |
|---|---|
| author | Wu, W.P. Yao, Z.Z. |
| author_facet | Wu, W.P. Yao, Z.Z. |
| citation_txt | Influence of a Strain Rate and Temperature on the Crack Tip Stress and Microstructure Evolution of Monocrystalline Nickel: a Molecular Dynamics Simulation / W.P. Wua, Z.Z. Yao // Проблемы прочности. — 2014. — № 2. — С. 12-21. — Бібліогр.: 31 назв. — англ. |
| collection | DSpace DC |
| container_title | Проблемы прочности |
| description | The effect of a strain rate and temperature on
the crack tip stress and microstructure evolution
ahead of a growing crack in monocrystalline
nickel are studied by molecular dynamics simulations.
The correlation between the microstructure
evolution and stress field near the crack tip
is also explored. The results indicate that the
crack tip stress distribution characteristics and
crack propagation dynamics are closely related
to the microstructure evolution caused by the
change of the strain rate and temperature. At a
lower strain rate and temperature, the crack propagates
by the brittle mechanism without inducing
the change in atomic configuration near the
crack tip. The stress concentration occurs at the
crack tip of a growing crack. The crack propagation
exhibits a gradual brittle-to-ductile transition
with an increase in temperature and a strain
rate. The peak stress is accompanied by the
microstructure evolution ahead of the crack tip.
Влияние скорости деформации и температуры на напряжение у вершины трещины и развитие микроструктуры вблизи распространяющейся трещины в монокристаллическом никеле
исследовали с помощью моделирования методом молекулярной динамики. Исследовали корреляцию между развитием микроструктуры и полем напряжений у вершины трещины. Результаты продемонстрировали, что характеристика распределения напряжений у вершины
трещины и динамика распространения трещины тесно связаны с развитием микроструктуры, обусловленной изменением скорости деформации и температуры. При низких скорости
деформации и температуре трещина распространяется по механизму хрупкого разрушения
без воздействия на изменение расположения атомов у ее вершины. Концентрация напряжений возникает у вершины распространяющейся трещины. Распространение трещины
характеризуется постепенным переходом от хрупкого разрушения к пластичному с увеличением температуры и скорости деформации. Максимальное напряжение сопровождается
развитием микроструктуры у вершины трещины.
Вплив швидкості деформації і температури на напруження у вістрі тріщини і розвиток мікроструктури поблизу тріщини, що розповсюджується, в монокристалічному
нікелі досліджували за допомогою моделювання методом молекулярної динаміки.
Досліджували кореляцію між розвитком мікроструктури і полем напружень у вістрі
тріщини. Результати показали, що характеристика розподілу напружень у вістрі
тріщини і динаміка поширення тріщини тісно пов’язані з розвитком мікроструктури,
зумовленої зміною швидкості деформації і температури. За низьких швидкості деформації і температури тріщина поширюється по механізму крихкого руйнування без
впливу на зміну розташування атомів у її вістрі. Концентрація напружень виникає у
вістрі тріщини, що поширюється. Поширення тріщини характеризується поступовим
переходом від крихкого руйнування до пластичного з підвищенням температури і
швидкості деформації. Максимальне напруження супроводжується розвитком мікроструктури у вістрі тріщини.
|
| first_indexed | 2025-12-01T16:34:41Z |
| format | Article |
| fulltext |
UDC 539.4
Influence of a Strain Rate and Temperature on the Crack Tip Stress and
Microstructure Evolution of Monocrystalline Nickel: a Molecular Dynamics
Simulation
W. P. Wu
a,1
and Z. Z. Yao
b
a Department of Engineering Mechanics, School of Civil Engineering, Wuhan University, Wuhan,
China
b Department of Mechanical Engineering, University of Wuppertal, Wuppertal, Germany
1 wpwu@whu.edu.cn
ÓÄÊ 539.4
Âëèÿíèå ñêîðîñòè äåôîðìàöèè è òåìïåðàòóðû íà íàïðÿæåíèå ó âåðøèíû
òðåùèíû è ðàçâèòèå ìèêðîñòðóêòóðû ìîíîêðèñòàëëè÷åñêîãî íèêåëÿ:
ìîäåëèðîâàíèå ìåòîäîì ìîëåêóëÿðíîé äèíàìèêè
Â. Ï. Âó
à,1
, Ç. Æ. ßî
á
à Ôàêóëüòåò òåîðåòè÷åñêîé ìåõàíèêè, êàôåäðà ãðàæäàíñêîãî ñòðîèòåëüñòâà, Óõàíüñêèé óíèâåð-
ñèòåò, Óõàíü, Êèòàé
á Ôàêóëüòåò ìàøèíîñòðîåíèÿ, Óíèâåðñèòåò Âóïïåðòàëÿ, Âóïïåðòàëü, Ãåðìàíèÿ
Âëèÿíèå ñêîðîñòè äåôîðìàöèè è òåìïåðàòóðû íà íàïðÿæåíèå ó âåðøèíû òðåùèíû è ðàçâè-
òèå ìèêðîñòðóêòóðû âáëèçè ðàñïðîñòðàíÿþùåéñÿ òðåùèíû â ìîíîêðèñòàëëè÷åñêîì íèêåëå
èññëåäîâàëè ñ ïîìîùüþ ìîäåëèðîâàíèÿ ìåòîäîì ìîëåêóëÿðíîé äèíàìèêè. Èññëåäîâàëè êîððå-
ëÿöèþ ìåæäó ðàçâèòèåì ìèêðîñòðóêòóðû è ïîëåì íàïðÿæåíèé ó âåðøèíû òðåùèíû. Ðåçóëü-
òàòû ïðîäåìîíñòðèðîâàëè, ÷òî õàðàêòåðèñòèêà ðàñïðåäåëåíèÿ íàïðÿæåíèé ó âåðøèíû
òðåùèíû è äèíàìèêà ðàñïðîñòðàíåíèÿ òðåùèíû òåñíî ñâÿçàíû ñ ðàçâèòèåì ìèêðîñòðóê-
òóðû, îáóñëîâëåííîé èçìåíåíèåì ñêîðîñòè äåôîðìàöèè è òåìïåðàòóðû. Ïðè íèçêèõ ñêîðîñòè
äåôîðìàöèè è òåìïåðàòóðå òðåùèíà ðàñïðîñòðàíÿåòñÿ ïî ìåõàíèçìó õðóïêîãî ðàçðóøåíèÿ
áåç âîçäåéñòâèÿ íà èçìåíåíèå ðàñïîëîæåíèÿ àòîìîâ ó åå âåðøèíû. Êîíöåíòðàöèÿ íàïðÿ-
æåíèé âîçíèêàåò ó âåðøèíû ðàñïðîñòðàíÿþùåéñÿ òðåùèíû. Ðàñïðîñòðàíåíèå òðåùèíû
õàðàêòåðèçóåòñÿ ïîñòåïåííûì ïåðåõîäîì îò õðóïêîãî ðàçðóøåíèÿ ê ïëàñòè÷íîìó ñ óâåëè-
÷åíèåì òåìïåðàòóðû è ñêîðîñòè äåôîðìàöèè. Ìàêñèìàëüíîå íàïðÿæåíèå ñîïðîâîæäàåòñÿ
ðàçâèòèåì ìèêðîñòðóêòóðû ó âåðøèíû òðåùèíû.
Êëþ÷åâûå ñëîâà: âåðøèíà òðåùèíû, àòîìíîå íàïðÿæåíèå, ðàçâèòèå ìèêðîñòðóêòóðû,
ìîíîêðèñòàëëè÷åñêèé íèêåëü, ìîäåëèðîâàíèå ìåòîäîì ìîëåêóëÿðíîé äèíàìèêè.
Introduction. The mechanical response of materials subject to applied stress is
controlled by atomistic mechanisms in the vicinity of stress concentrations such as crack
tips. Crack tips represent mathematical singularities for the stress distribution, providing
local large interatomic forces that form the seeds for macroscopic failure [1, 2]. Crack tip
behavior in metals is among the most basic problems in mechanics of materials. A material
exhibits intrinsically brittle behavior if an existing crack can propagate along certain
crystallographic planes in a cleavage manner, whereas ductile fracture occurs when there is
plastic deformation at the crack tip. The plastic processes at the crack tips, including
dislocation emission, void nucleation, twinning, etc. have a pronounced effect on the crack
© W. P. WU, Z. Z. YAO, 2014
12 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2014, ¹ 2
propagation and stress distribution around the growing crack. When a pre-cracked crystal
deforms plastically in the crack tip region within a certain range of temperature and strain
rate, inhomogeneous dislocations are generated as a diverse form in the crystal [3]. At the
macroscale, the strain rate and temperature effects have been studied for many ductile
metals [4–7]. At the atomic scale, the response of fracture in the crystal metals to the strain
rate and temperature is a complicated phenomenon, involving many micromechanisms,
such as dislocation motions [8–10], twins [11–13], stacking faults [13], slip [14, 15], etc.
This microstructural evolution of atoms around the crack tip may result in a change of the
stress field around the crack tip and severely affect the fracture properties of material, such
as the twins and dislocation slip, which may be considered as a contributing deformation
mechanism and significantly affect the crack propagation [16]. At present, atomistic
simulations have proved to be a useful tool for studying the crack tip plasticity and fracture
properties of materials by investigating atomistic configuration and stress field around the
crack tip from an atomistic standpoint [17–20]. Moreover, atomistic simulations of fracture
events have produced observations that resemble characteristics at the macroscopic scales
and yielded an important finding from atomistic simulation is that atomic stress plays a
controlling role in nanoscale fracture [21–24]. Considering the strain rate and temperature
have a significant effect on the crack tip plasticity and atomic stress field at the atomic
scale, it is believed that the apparently large discrepancy among the crack tip plasticity and
stress field exists at different temperatures and strain rates, which results in different crack
tip microstructures and nanoscale fracture mechanisms. Therefore, it is necessary to
investigate the effect of temperature and strain rate on the stress field and microstructure
evolution near the crack tip, and it is also essential and important for understanding the
nanoscale fracture properties at different strain rates and temperatures.
In this paper, we carry out molecular dynamics (MD) simulations to investigate the
internal microstructure evolution and atomic stress distribution near the crack tip during
crack propagation at different strain rates and temperatures. The objective of the present
work is to characterize the influence of strain rate and temperature on the stress and
microstructure evolution near the crack tip during crack propagation, as well as to
determine the relationship between the change of the stress field near the crack tip and
microstructure evolution at different strain rates and temperatures. Meanwhile, it also offers
an explanation for the influence of the internal microstructure evolution on the crack
opening displacement.
1. Atomistic Model and Simulation Process. In this work, we perform a MD
simulation to investigate the effects of temperature and strain rate on crack tip stress and
microstructure evolution of a growing crack in a pre-cracked single crystal nickel. The MD
simulation describes motions of all atoms in a system by numerically solving Newton’s
equations and determines the material property by the inter-atomic potentials. For face-
centered cubic (fcc) metallic materials the embedded-atom-method (EAM) is one of the
most popular inter-atomic potentials [25, 26]. The EAM potential proposed by Mishin et al.
[27] is used here to simulate failure process of a pre-cracked single crystal nickel,
considering that this potential is lucrative for description of the bonding in metallic systems
and gives a reasonable simulation of fracture and damage. In this MD simulation, a
constrained three-dimensional model is employed for the study of crack propagation and
failure process in fcc single crystal nickel at various temperatures and strain rates. The
geometry of the crack propagation system is shown in Fig. 1a.
The crystal has a cubic orientation (i.e., X �[ ],100 Y �[ ],010 and Z�[ ]001). The
crystal dimension in the X-axis is chosen to be sufficiently large so that steady-state crack
propagation is obtained during MD simulations. The atoms in the top and bottom layers,
which have a thickness of potential cut-off distance, are fixed. Periodic boundary conditions
are formulated in the X and Z directions, and non-periodic boundary conditions are applied
in the Y direction. In the model (Fig. 1a), a single crack is inserted into the center of crystal
Influence of Strain Rate and Temperature ...
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2014, ¹ 2 13
by removing atoms, the size of the model is 150 100 6a a a� � (528 Å�352 Å�21.12 Å),
while the initial crack length is equal to 10a (35.2 Å), and its width – to the lattice
constant of nickel a (a =3.52 Å). The initial atomic configuration near the crack tip is
shown in Fig. 1b. To study the effects of strain rate and temperature on the stress and
microstructure evolution near the crack tip during crack propagation, we set up four
different strain rates 1 108� , 2 108� , 5 108� , and 1 109 1� �s and four different temperatures
5, 100, 300, and 500 K, respectively. At the start of simulation, this atomic system is
relaxed using the conjugate gradient method to reach the minimum energy state. Then the
relaxed system is stretched in the Y direction by an incrementally displacement loading
every 20 ps, by keeping the top and bottom boundaries parallel. The deformed configuration
of the system is computed by the MD simulation, which is carried out by integrating
Newton’s equations of motion for all atoms using a time step of 1 10 15� � s. The open
source MD code LAMMPS [28] and the AtomEye visualization tools [29] are used in the
atomistic simulations.
To study the nanoscale fracture behavior and analyze the atomic stress fields near the
crack tip in the process of fracture, the atomistic stress definition is employed in this work.
The atomic stress at an atom i is a stress quantity at the atomic scale. This is the strength
measurement of the interatomic interactions of the atom with its neighboring atoms. This
atomic stress tensor is defined in the component form by the following equation [30]:
� �� � �( ) ( , ) ( , ),
( )
i f i j r i j
i j i
N
��
1
2�
(1)
W. P. Wu and Z. Z. Yao
14 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2014, ¹ 2
a
b
Fig. 1. Atomistic model: (a) sample geometry of a fcc single crystal nickel containing a single
centered crack and (b) initial atomic configuration.
where � i is the volume of atom i (� i iR�
4
3
3� , Ri is the radius of atom i), N is the
number of atoms in a region around atom i within the EAM potential cut-off distance
(which is 4.80 Å for Ni), f i j� ( , ) is the vector component form of the interaction force
exerted by atom j to atom i, whereas r i j� ( , ) is the vector component form of the relative
position from atom j to atom i.
Taking an average value over the volume around atom i within the potential cut-off
distance, the average atomic stress tensor � �� for atom i is given by [31]:
� ��� ��( ) ( ).i
N
j
j
N
�
�
1
1
(2)
2. Simulation Results.
2.1. Effect of Strain Rate on the Crack Tip Stress and Microstructure Evolution.
Figure 2 presents a detailed observation on the stress distributions and atomic configurations
around the crack tip for four different strain rates at 5 K. When the crystal is stretched to
the same amount of strain
� 0.07 at four different strain rates, the crack tip atoms exhibit
different configurations and stress levels. For a lower strain rate (1 108 1� �s ), the crack is
extended at a considerable distance and approaches fracture. The stress is concentrated
directly at the crack tip without inducing the change of atomic configuration as shown in
Fig. 2a. At the strain rate of 2 108 1� �s , the atomic configuration and stress distribution at
the crack tip are similar to those at a lower strain rate of 1 108 1� �s , but the crack length is
smaller and the peak stress value at the crack tip is lower (Fig. 2b). With the increase in the
strain rate, it is found that the crack propagation increment at a lower strain rate of
2 108 1� �s is larger than those at higher strain rates (5 108� and 1 109 1� �s ), while the peak
stress at the crack tip is also higher, as shown in Fig. 2b–d. Moreover, it is also observed
that the change of atomic configuration at the crack tip at a higher strain rate when the
strain reaches the same value
� 0.07, the crack tip blunting occurs ahead of a growing
crack due to the dislocation emission at a higher strain rate of 1 109 1� �s . This reveals that
the crack tip microstructure evolution is easier to occur at a higher strain rate when the
strain reaches the same value. As it was observed above, at lower strain rates the crack
propagation occured by the brittle mechanism without inducing any microstructure evolution
in the single crystal nickel at 5 K. The stress is always concentrated at the crack tip of
growing crack through the crack propagation process. With increase in the strain rate, the
crack propagation behavior exhibits a gradually developing transition from brittle to ductile
pattern, the dislocations are emitted at the crack tip and induce the crack tip blunting, while
the peak stress occurs in the crack-blunting region surrounding the crack front.
2.2. Effect of Temperature on the Crack Tip Stress and Microstructure Evolution.
For the loading time of t � 360 ps, Fig. 3 shows the crack propagation states, stress
distributions and microstructure characteristics near the crack tip at the same strain rate of
2 108 1� �s and different temperatures. At the temperature of T � 5 K, the stress
concentration occurs at the crack tip without inducing any microstructure evolution, as is
shown in Fig. 3a. When the temperature is increased, the ability of atomic motion is
enhanced, and dislocations become more mobile due to the thermal activation, whereas the
atomic configuration is also changed at elevated temperature. At T � 100 K, the atomic
configuration near the crack tip is changed, a void is formed where the atomic tensile stress
has the highest value at a certain distance ahead of the crack tip, this peak stress being
accompanied by the appearance of the void at the location of the stress concentration
(Fig. 3b). At T � 300 K, it is observed that numerous dislocations are emitted ahead of the
Influence of Strain Rate and Temperature ...
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2014, ¹ 2 15
crack tip, which dislocations hinder the crack propagation along the original direction. It is
recognized that atoms in the region of microstructure evolution have significantly higher
stress and energy values than bulk atoms, whereas the crack is expected to propagate along
the direction where the newly created surface energy is the lowest, so the crack propagation
deviates from the original direction as shown in Fig. 3c. When temperature is further
increased, the atoms near the crack tip emit a larger number of dislocations and induce the
crack tip blunting at T � 500 K. The crack propagation becomes slower at a higher
temperature of T � 500 K due to the crack blunting surrounding the crack front. The
concentration of the atomic tensile stress occurs in a blunting region ahead of the crack tip,
and the peak stress is about 17 GPa as shown in Fig. 3d. The analysis of the microstructure
characteristics testifies that the temperature change induces the microstructure evolution
(dislocation generation or void nucleation) at a certain distance ahead of the crack tip.
Simultaneously, the microstructure evolution induces the variation of the stress field around
the crack tip. Figure 3 shows a one-to-one relationship between the stress distributions and
microstructure characteristics near the crack tip at different temperatures. These are plots of
W. P. Wu and Z. Z. Yao
16 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2014, ¹ 2
Fig. 2. Contour plots of the atomic tensile stress distributions and microstructures near right hand
crack tip at strain
� 0.07 for different strain rates: (a) 1 108 1� �s ; (b) 2 108 1� �s ; (c) 5 108 1� �s ;
(d) 1 109 1� �s .
the stress field and microstructure evolution at different temperatures illustrating different
crack tip plasticity and crack propagation process. There is a gradual change of influence
from dislocation non-generation at 5 K to the void formation and crack tip blunting
surrounding the crack front with increasing temperature.
2.3. Crack Opening Displacement at Different Strain Rates and Temperatures.
Crack opening displacement (COD) is an important aspect for understanding the crack
growth and fracture behavior. In order to show quantitatively the strain rate and temperature
effects on the crack resistance and crack propagation dynamics, COD is calculated at
different strain rates and temperatures. The results for the COD as a function of atom
position for different strain rates and temperatures are shown in Fig. 4. When the strain
reaches the same value
� 0.07 at four different strain rates, it can be seen that the COD
has the maximum value (approximately 9 Å) at the lower strain rate of 1 108 1� �s , and the
COD pattern along the crack path has a symmetry relative to the crack center. The COD
value decreases with increase in the strain rate, and the COD along the crack path becomes
more and more asymmetrical (Fig. 4a). The main reason for the COD variation is the
Influence of Strain Rate and Temperature ...
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2014, ¹ 2 17
Fig. 3. Contour plots of the atomic tensile stress distributions and microstructures near right hand
crack tip at loading time of t � 360 ps and different temperatures: (a) T � 5 K; (b) T �100 K;
(c) T � 300 K; (d) T � 500 K.
microstructure evolution near the crack tip at the higher strain rate. Figure 4b shows the
COD as a function of atom position at the loading time of t � 360 ps and different
temperatures. At T � 5 K, the COD is about 7 Å, and the COD along the crack path is
symmetrical relative to the crack center. The COD increases with the temperature increase,
and the largest COD value of 16 Å is attained at T � 300 K, while the COD along the crack
tip becomes asymmetric due to the fact that temperature variation induces the microstructure
evolution near the crack tip. When the temperature is raised to 500 K, the COD is about
9 Å, the crack arrests and hardly propagates at the same loading time (t � 360 ps) because
of a larger number of dislocation emissions at the crack front hindering the crack
propagation. The above results indicate that the COD is closely related to the micro-
structure evolution near the crack tip for different strain rates and temperatures.
Conclusions. The MD simulations have been performed to study crack tip stress and
microstructure evolution of a pre-cracked single crystal nickel at different strain rates and
temperatures. The results indicate that the strain rate and temperature have a strong effect
on the crack tip stress and microstructure evolution. When the same value of deformation is
reached at different strain rates, in case of lower strain rates, the crack propagates rapidly
without inducing any microstructure evolution at the crack tip, while the stress concentration
occurs at the crack tip of a growing crack. At increased strain rates, the crack propagation
becomes slower due to the change of atomic configuration at the crack tip. There is a
gradually developing transition from brittle to ductile pattern, where the dislocations are
emitted at the crack tip and induce the crack tip blunting, the peak stress occurring in the
crack blunting region. For different temperatures, it is shown that crack propagates rapidly
in a brittle manner at 5 K, and the stress is directly concentrated at the crack tip without
inducing the change of atomic configuration. Crack propagation becomes slower or
deviates from the original crack path at elevated temperatures due to the microstructure
evolution ahead of the crack tip. In this case, the peak stress occurs at the location of the
microstructure evolution. With further increase in the temperature, the crack arrests and
hardly propagates due to the fact that emitted dislocations induce crack tip blunting at the
crack front. Furthermore, the crack opening displacement and the stress field variations at
different strain rates and temperatures are shown to be closely related to the microstructure
evolution near the crack tip caused by the strain rate and temperature variations.
The presented results have been obtained for a special atomistic configuration and a
certain range of strain rates and temperatures. The crystal orientation, the atomic potential
and constrain conditions, etc. also influence the crack tip stress and microstructure
evolution. A more detailed and extensive MD model is necessary to provide more general
W. P. Wu and Z. Z. Yao
18 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2014, ¹ 2
a b
Fig. 4. Crack opening displacement (COD) as a function of atom position for a single crystal nickel:
(a) at different strain rates; (b) at different temperatures.
insight into the crack tip stress and microstructure evolution characteristics at the atomic
level.
Acknowledgements. The work was supported by National Natural Science Foundation
of China (Grant No. 11102139), and China Postdoctoral Science Foundation (Grant
Nos. 20110491205 and 2012T50665).
Ð å ç þ ì å
Âïëèâ øâèäêîñò³ äåôîðìàö³¿ ³ òåìïåðàòóðè íà íàïðóæåííÿ ó â³ñòð³ òð³ùèíè ³ ðîçâè-
òîê ì³êðîñòðóêòóðè ïîáëèçó òð³ùèíè, ùî ðîçïîâñþäæóºòüñÿ, â ìîíîêðèñòàë³÷íîìó
í³êåë³ äîñë³äæóâàëè çà äîïîìîãîþ ìîäåëþâàííÿ ìåòîäîì ìîëåêóëÿðíî¿ äèíàì³êè.
Äîñë³äæóâàëè êîðåëÿö³þ ì³æ ðîçâèòêîì ì³êðîñòðóêòóðè ³ ïîëåì íàïðóæåíü ó â³ñòð³
òð³ùèíè. Ðåçóëüòàòè ïîêàçàëè, ùî õàðàêòåðèñòèêà ðîçïîä³ëó íàïðóæåíü ó â³ñòð³
òð³ùèíè ³ äèíàì³êà ïîøèðåííÿ òð³ùèíè ò³ñíî ïîâ’ÿçàí³ ç ðîçâèòêîì ì³êðîñòðóêòóðè,
çóìîâëåíî¿ çì³íîþ øâèäêîñò³ äåôîðìàö³¿ ³ òåìïåðàòóðè. Çà íèçüêèõ øâèäêîñò³ äå-
ôîðìàö³¿ ³ òåìïåðàòóðè òð³ùèíà ïîøèðþºòüñÿ ïî ìåõàí³çìó êðèõêîãî ðóéíóâàííÿ áåç
âïëèâó íà çì³íó ðîçòàøóâàííÿ àòîì³â ó ¿¿ â³ñòð³. Êîíöåíòðàö³ÿ íàïðóæåíü âèíèêຠó
â³ñòð³ òð³ùèíè, ùî ïîøèðþºòüñÿ. Ïîøèðåííÿ òð³ùèíè õàðàêòåðèçóºòüñÿ ïîñòóïîâèì
ïåðåõîäîì â³ä êðèõêîãî ðóéíóâàííÿ äî ïëàñòè÷íîãî ç ï³äâèùåííÿì òåìïåðàòóðè ³
øâèäêîñò³ äåôîðìàö³¿. Ìàêñèìàëüíå íàïðóæåííÿ ñóïðîâîäæóºòüñÿ ðîçâèòêîì ì³êðî-
ñòðóêòóðè ó â³ñòð³ òð³ùèíè.
1. J. R. Rice and R. Thomson, “Ductile versus brittle behavior of crystals,” Phil. Mag.,
29, Issue 1, 73–97 (1974).
2. M. J. Buehler and H. Gao, “Dynamical fracture instabilities due to local hyperelasticity
at crack tips,” Nature, 439, 307–310 (2006).
3. S. M. Byon, H. S. Kim, and Y. Lee, “Investigation of the size effect on the crack
propagation using finite element method and strain gradient plasticity,” J. Mater.
Process. Technol., 191, No. 1-3, 193–197 (2007).
4. D. H. Sastry, Y. V. R. K. Prasad, and S. C. Deevi, “Influence of temperature and
strain rate on the flow stress of an FeAl alloy,” Mater. Sci. Eng. A, 299, No. 1-2,
157–163 (2001).
5. M. Shazly, V. Prakash, and S. Draper, “Mechanical behavior of Gramma-Met PX
under uniaxial loading at elevated temperatures and high strain rates,” Int. J. Solids
Struct., 41, No. 22-23, 6485–6503 (2004).
6. I. M. Low and Y. W. Mai, “Rate and temperature effects on crack blunting
mechanisms in pure and modified epoxies,” J. Mater. Sci., 24, No. 5, 1634–1644
(1989).
7. F. Massa, R. Piques, and A. Laurent, “Rapid crack propagation in polyethylene pipe:
combined effect of strain rate and temperature on fracture toughness,” J. Mater. Sci.,
32, No. 24, 6583–6587 (1997).
8. J. R. Rice, “Dislocation nucleation from a crack tip: An analysis based on the peierls
concept,” J. Mech. Phys. Solids, 40, No. 12, 239–271 (1992).
9. W. P. Wu, Y. F. Guo, and Y. S. Wang, “Evolution of misfit dislocation network and
tensile properties in Ni-based superalloys: a molecular dynamics simulation,” Sci.
China-Phys. Mech. Astron., 55, No. 3, 419–427 (2012).
10. V. Yamakov, D. Wolf, M. Salazar, et al., “Length-scale effects in the nucleation of
extended dislocations in nanocrystalline Al by molecular dynamics simulation,” Acta
Mater., 49, No. 14, 2713–2722 (2001).
Influence of Strain Rate and Temperature ...
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2014, ¹ 2 19
11. R. P. Reed, “Deformation twinning in Ni and F.C.C. Fe–Ni alloys,” Phil. Mag., 15,
No. 137, 1051–1055 (1967).
12. P. Haasen, “Plastic deformation of nickel single crystals at low temperatures,” Phil.
Mag., 3, No. 28, 384–418 (1958).
13. Y. F. Guo, C. Y. Wang, and Y. S. Wang, “The effect of stacking fault or twin
formation on bcc-iron crack propagation,” Phil. Mag. Lett., 84, No. 12, 763–770
(2004).
14. H. Traub, H. Neuhauser, and C. H. Schwink, “Investigations of the yield region of
concentrated Cu–Ge and Cu–Zn single crystals – I. Critical resolved shear stress, slip
line formation and the true strain rate,” Acta Metall., 25, No. 4, 437–446 (1977).
15. C. Atkinson and C. Bastero, “Plastic relaxation at a crack tip by asymmetric slip,”
Proc. Roy. Soc. London A, 418, 261–280 (1854).
16. D. H. Warner, W. A. Curtin, and S. Qu, “Rate dependence of crack tip processes
predicts twinning trends in f.c.c. metals,” Nature Mater., 6, No. 11, 876–881 (2007).
17. K. S. Cheung and S. Yip, “A molecular-dynamics simulation of crack tip extension:
the brittle-to ductile transition,” Model. Simul. Mater. Sci. Eng., 2, No. 4, 865–892
(1994).
18. T. Kitamura, K. Yashiro, and R. Ohtani, “Atomic simulation on deformation and
fracture of nano-single crystal of nickel in tension,” JSME Int. J., Ser. A., 40, No. 4,
430–435 (1997).
19. C. W. Pao, S. M. Foiles, E. B. Webb III, et al., “Atomistic simulations of stress and
microstructure evolution during polycrystalline Ni film growth,” Phys. Rev. B, 79,
No. 2, 224113 (2009).
20. R. Matsumoto, M. Nakagaki, A. Nakatani, and H. Kitagawa, “Molecular-dynamics
study on crack growth behavior relevant to crystal nucleation in amorphous metal,”
CMES: Computer Modeling in Engineering & Sciences, 9, No. 1, 75–84 (2005).
21. M. J. Buehler, H. Gao, and Y. Huang, “Atomistic and continuum studies of stress and
strain fields near a rapidly propagating crack in a harmonic lattice,” Theor. Appl.
Fract. Mech., 41, No. 1-3, 21–42 (2004).
22. H. Krull and H. Yuan, “Suggestions to the cohesive traction-separation law from
atomistic simulations,” Eng. Fract. Mech., 78, No. 3, 525–533 (2011).
23. S. Xu and X. Deng, “Nanoscale void nucleation and growth and crack tip stress
evolution ahead of a growthing crack in a single crystal,” Nanotechnology, 19, No. 11,
115705, DOI: 10.1088/0957-4484/19/11/115705 (2008).
24. W. P. Wu and Z. Z. Yao, “Molecular dynamics simulation of crack tip stress and
microstructure evolution of a growing crack in single crystal nickel,” Theor. Appl.
Fract. Mech., 62, No. 12, 67–75 (2012).
25. M. S. Daw, S. M. Foiles, and M. I. Baskes, “The embedded-atom method: a review of
theory and applications,” Mater. Sci. Rep., 9, No. 7-8, 251–310 (1993).
26. M. F. Horstemeyer, M. I. Baskes, and S. J. Plimpton, “Computational nanoscale
plasticity simulations using embedded atom potentials,” Theor. Appl. Fract. Mech.,
37, No. 1, 49–98 (2001).
27. Y. Mishin, D. Farkas, M. J. Mehl, and D. A. Papaconstantopoulos, “Interatomic
potentials for monatomic metals from experimental data and ab initio calculations,”
Phys. Rev. B, 59, No. 5, 3393–3407 (1999).
28. S. J. Plimpton, “Fast parallel algorithms for short-range molecular dynamics,” J.
Comput. Phys., 117, 1–19 (1995).
W. P. Wu and Z. Z. Yao
20 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2014, ¹ 2
29. J. Li, “AtomEye: an efficient atomistic configuration viewer,” Model. Simul. Mater.
Sci. Eng., 11, 173–177 (2003).
30. M. Born and K. Huang, Dynamical Theory of Crystal Lattices, Clarendon, Oxford
(1954).
31. M. F. Horstemeyer and M. I. Baskes, “Atomistic finite deformation simulations: a
discussion on length scale effects in relation to mechanical stresses,” J. Eng. Mater.
Technol., 121, No. 2, 114–119 (1999).
Received 22. 11. 2013
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2014, ¹ 2 21
Influence of Strain Rate and Temperature ...
|
| id | nasplib_isofts_kiev_ua-123456789-112702 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 0556-171X |
| language | English |
| last_indexed | 2025-12-01T16:34:41Z |
| publishDate | 2014 |
| publisher | Інститут проблем міцності ім. Г.С. Писаренко НАН України |
| record_format | dspace |
| spelling | Wu, W.P. Yao, Z.Z. 2017-01-26T18:09:50Z 2017-01-26T18:09:50Z 2014 Influence of a Strain Rate and Temperature on the Crack Tip Stress and Microstructure Evolution of Monocrystalline Nickel: a Molecular Dynamics Simulation / W.P. Wua, Z.Z. Yao // Проблемы прочности. — 2014. — № 2. — С. 12-21. — Бібліогр.: 31 назв. — англ. 0556-171X https://nasplib.isofts.kiev.ua/handle/123456789/112702 539.4 The effect of a strain rate and temperature on the crack tip stress and microstructure evolution ahead of a growing crack in monocrystalline nickel are studied by molecular dynamics simulations. The correlation between the microstructure evolution and stress field near the crack tip is also explored. The results indicate that the crack tip stress distribution characteristics and crack propagation dynamics are closely related to the microstructure evolution caused by the change of the strain rate and temperature. At a lower strain rate and temperature, the crack propagates by the brittle mechanism without inducing the change in atomic configuration near the crack tip. The stress concentration occurs at the crack tip of a growing crack. The crack propagation exhibits a gradual brittle-to-ductile transition with an increase in temperature and a strain rate. The peak stress is accompanied by the microstructure evolution ahead of the crack tip. Влияние скорости деформации и температуры на напряжение у вершины трещины и развитие микроструктуры вблизи распространяющейся трещины в монокристаллическом никеле исследовали с помощью моделирования методом молекулярной динамики. Исследовали корреляцию между развитием микроструктуры и полем напряжений у вершины трещины. Результаты продемонстрировали, что характеристика распределения напряжений у вершины трещины и динамика распространения трещины тесно связаны с развитием микроструктуры, обусловленной изменением скорости деформации и температуры. При низких скорости деформации и температуре трещина распространяется по механизму хрупкого разрушения без воздействия на изменение расположения атомов у ее вершины. Концентрация напряжений возникает у вершины распространяющейся трещины. Распространение трещины характеризуется постепенным переходом от хрупкого разрушения к пластичному с увеличением температуры и скорости деформации. Максимальное напряжение сопровождается развитием микроструктуры у вершины трещины. Вплив швидкості деформації і температури на напруження у вістрі тріщини і розвиток мікроструктури поблизу тріщини, що розповсюджується, в монокристалічному нікелі досліджували за допомогою моделювання методом молекулярної динаміки. Досліджували кореляцію між розвитком мікроструктури і полем напружень у вістрі тріщини. Результати показали, що характеристика розподілу напружень у вістрі тріщини і динаміка поширення тріщини тісно пов’язані з розвитком мікроструктури, зумовленої зміною швидкості деформації і температури. За низьких швидкості деформації і температури тріщина поширюється по механізму крихкого руйнування без впливу на зміну розташування атомів у її вістрі. Концентрація напружень виникає у вістрі тріщини, що поширюється. Поширення тріщини характеризується поступовим переходом від крихкого руйнування до пластичного з підвищенням температури і швидкості деформації. Максимальне напруження супроводжується розвитком мікроструктури у вістрі тріщини. The work was supported by National Natural Science Foundation of China (Grant No. 11102139), and China Postdoctoral Science Foundation (Grant Nos. 20110491205 and 2012T50665). en Інститут проблем міцності ім. Г.С. Писаренко НАН України Проблемы прочности Научно-технический раздел Influence of a Strain Rate and Temperature on the Crack Tip Stress and Microstructure Evolution of Monocrystalline Nickel: a Molecular Dynamics Simulation Влияние скорости деформации и температуры на напряжение у вершины трещины и развитие микроструктуры монокристаллического никеля: моделирование методом молекулярной динамики Article published earlier |
| spellingShingle | Influence of a Strain Rate and Temperature on the Crack Tip Stress and Microstructure Evolution of Monocrystalline Nickel: a Molecular Dynamics Simulation Wu, W.P. Yao, Z.Z. Научно-технический раздел |
| title | Influence of a Strain Rate and Temperature on the Crack Tip Stress and Microstructure Evolution of Monocrystalline Nickel: a Molecular Dynamics Simulation |
| title_alt | Влияние скорости деформации и температуры на напряжение у вершины трещины и развитие микроструктуры монокристаллического никеля: моделирование методом молекулярной динамики |
| title_full | Influence of a Strain Rate and Temperature on the Crack Tip Stress and Microstructure Evolution of Monocrystalline Nickel: a Molecular Dynamics Simulation |
| title_fullStr | Influence of a Strain Rate and Temperature on the Crack Tip Stress and Microstructure Evolution of Monocrystalline Nickel: a Molecular Dynamics Simulation |
| title_full_unstemmed | Influence of a Strain Rate and Temperature on the Crack Tip Stress and Microstructure Evolution of Monocrystalline Nickel: a Molecular Dynamics Simulation |
| title_short | Influence of a Strain Rate and Temperature on the Crack Tip Stress and Microstructure Evolution of Monocrystalline Nickel: a Molecular Dynamics Simulation |
| title_sort | influence of a strain rate and temperature on the crack tip stress and microstructure evolution of monocrystalline nickel: a molecular dynamics simulation |
| topic | Научно-технический раздел |
| topic_facet | Научно-технический раздел |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/112702 |
| work_keys_str_mv | AT wuwp influenceofastrainrateandtemperatureonthecracktipstressandmicrostructureevolutionofmonocrystallinenickelamoleculardynamicssimulation AT yaozz influenceofastrainrateandtemperatureonthecracktipstressandmicrostructureevolutionofmonocrystallinenickelamoleculardynamicssimulation AT wuwp vliânieskorostideformaciiitemperaturynanaprâženieuveršinytreŝinyirazvitiemikrostrukturymonokristalličeskogonikelâmodelirovaniemetodommolekulârnoidinamiki AT yaozz vliânieskorostideformaciiitemperaturynanaprâženieuveršinytreŝinyirazvitiemikrostrukturymonokristalličeskogonikelâmodelirovaniemetodommolekulârnoidinamiki |