Effect of the Microcrack Inclination Angle on Crack Propagation Behavior of TiAl Alloy
Molecular dynamics simulation was employed to make the model of crack propagation for singlecrystal y-TiAl alloy. The effects of the angle between a microcrack and loading direction on crack propagation were studied through the analysis of the atomic configurations and stress—strain curves in the pa...
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nasplib_isofts_kiev_ua-123456789-1735862025-02-23T20:14:27Z Effect of the Microcrack Inclination Angle on Crack Propagation Behavior of TiAl Alloy Анализ влияния угла наклона микротрещины на характеристики роста трещин в сплаве TiAl Feng, R.C. Lu, J.T. Li, H.Y. Cao, H. Rui, Z.Y. Научно-технический раздел Molecular dynamics simulation was employed to make the model of crack propagation for singlecrystal y-TiAl alloy. The effects of the angle between a microcrack and loading direction on crack propagation were studied through the analysis of the atomic configurations and stress—strain curves in the paper. The results show that the time for the emission of first dislocation and the yield stress value decrease with the angle. The crack propagation occurs by the submain crack mechanism, which becomes more obvious as the angle increases and the number of stacking faults and stair-rod dislocations decreases. This work was financially supported by National Natural Science Foundation of Gansu Province, China (No. 148RJZA008), Research project of Gansu Province, China (No. 2014A-033) and Doctoral research fundation of L anzhou University of Technology. Feng Ruicheng would like to thank Key Laboratory of Digital Manufacturing Technology and Application, the Ministry of Education, Lanzhou University of Technology for providing help. 2017 Article Effect of the Microcrack Inclination Angle on Crack Propagation Behavior of TiAl Alloy / R.C. Feng, J.T. Lu, H.Y. Li, H. Cao, Z.Y. Rui // Проблемы прочности. — 2017. — № 1. — С. 87-94. — Бібліогр.: 25 назв. — англ. 0556-171X https://nasplib.isofts.kiev.ua/handle/123456789/173586 539.4 en Проблемы прочности application/pdf Інститут проблем міцності ім. Г.С. Писаренко НАН України |
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Научно-технический раздел Научно-технический раздел Feng, R.C. Lu, J.T. Li, H.Y. Cao, H. Rui, Z.Y. Effect of the Microcrack Inclination Angle on Crack Propagation Behavior of TiAl Alloy Проблемы прочности |
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Molecular dynamics simulation was employed to make the model of crack propagation for singlecrystal y-TiAl alloy. The effects of the angle between a microcrack and loading direction on crack propagation were studied through the analysis of the atomic configurations and stress—strain curves in the paper. The results show that the time for the emission of first dislocation and the yield stress value decrease with the angle. The crack propagation occurs by the submain crack mechanism, which becomes more obvious as the angle increases and the number of stacking faults and stair-rod dislocations decreases. |
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Article |
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Feng, R.C. Lu, J.T. Li, H.Y. Cao, H. Rui, Z.Y. |
| author_facet |
Feng, R.C. Lu, J.T. Li, H.Y. Cao, H. Rui, Z.Y. |
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Feng, R.C. |
| title |
Effect of the Microcrack Inclination Angle on Crack Propagation Behavior of TiAl Alloy |
| title_short |
Effect of the Microcrack Inclination Angle on Crack Propagation Behavior of TiAl Alloy |
| title_full |
Effect of the Microcrack Inclination Angle on Crack Propagation Behavior of TiAl Alloy |
| title_fullStr |
Effect of the Microcrack Inclination Angle on Crack Propagation Behavior of TiAl Alloy |
| title_full_unstemmed |
Effect of the Microcrack Inclination Angle on Crack Propagation Behavior of TiAl Alloy |
| title_sort |
effect of the microcrack inclination angle on crack propagation behavior of tial alloy |
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Інститут проблем міцності ім. Г.С. Писаренко НАН України |
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2017 |
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Научно-технический раздел |
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Effect of the Microcrack Inclination Angle on Crack Propagation Behavior of TiAl Alloy / R.C. Feng, J.T. Lu, H.Y. Li, H. Cao, Z.Y. Rui // Проблемы прочности. — 2017. — № 1. — С. 87-94. — Бібліогр.: 25 назв. — англ. |
| series |
Проблемы прочности |
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2025-11-25T00:07:24Z |
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2025-11-25T00:07:24Z |
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1849718729085026304 |
| fulltext |
UDC 539.4
Effect of the Microcrack Inclination Angle on Crack Propagation Behavior of
TiAl Alloy
R . C. F eng ,a b J . T . L u ,ab1 H . Y. L i,ab H . C ao ,a b an d Z . Y. R u ia b
a Key Laboratory of Digital Manufacturing Technology and Application, the Ministry of Education,
Lanzhou University of Technology, Lanzhou, China
b School of Mechanical and Electronical Engineering, Lanzhou University of Technology, Lanzhou,
China
1 Lujiant@163.com
Molecular dynamics simulation was employed to make the model o f crack propagation fo r single
crystal y-TiAl alloy. The effects o f the angle between a microcrack and loading direction on crack
propagation were studied through the analysis o f the atomic configurations and stress—strain curves
in the paper. The results show that the time fo r the emission o f first dislocation and the yield stress
value decrease with the angle. The crack propagation occurs by the submain crack mechanism,
which becomes more obvious as the angle increases and the number o f stacking faults and stair-rod
dislocations decreases.
K eyw ords: m icrocrack, y-TiAl alloy, crack propagation, m olecular dynamics.
In tro d u c tio n . Because o f low density, high specific stiffness, good high temperature
strength, and creep resistance, y-TiAl alloys are w idely used in the aerospace industry [1,
2]. However, life o f structural com ponents is controlled by crack initiation and propagation
under loading conditions. A large num ber o f experim ents showed that crack initiation
greatly reduced the m echanical properties o f m aterial and directly affected the residual life,
while m any scholars focus their studies on the crack propagation stage [3]. However, due to
the developm ent o f the com puter technologies, the m olecular dynam ics m ethod has been
introduced as an im portant research tool in the m aterials science field [4].
A t present, scholars have done a lot o f research on crack propagation using the
m olecular dynam ics method. Terentyev et al. [5] investigated the effects o f the strain rate,
tem perature and the crack shape on crack propagation behavior o f bcc and fcc metals, and
the conclusion that bcc m etals are m ore prone to brittle fracture rather than ductile one. For
fcc metals, w hen dislocations are emitted, the crack tip is blunted. Zhou et al. [6] studied
the effects o f grain boundaries on crack propagation behavior o f bicrystal m agnesium , and
found that as the grain boundary angle increases, crack experiences the sharpening-
blunting-sharpening cyclic variations. K arim i et al. [7] analyzed the crack propagation
behavior o f single-crystal nickel w ith defects using the m olecular dynam ics method. Yan et
al. [8] investigated the effects o f tem perature on crack propagation m echanism o f single
crystal alum inum w ith the edge crack or center crack, and concluded that the edge crack
yield stress is higher than that o f the central crack at low tem perature, but w ith an increase
in tem perature, the result is contrary. Guo [9] sim ulated the m ode I crack propagation
process o f single-crystal Si and A l using m olecular dynam ics method, and showed that
crack does not propagate by the cleavage m echanism , but becom es blunted because o f
dislocation em ission from the crack tip, and a disordered region is form ed due to the
pile-up o f disordered atoms at the crack tip. The crack propagates by m eans o f the driving
force m oving the disordered regions. Rafii-Tabar et al. [10] and M ousazadeh and Dehghani
[11] studied the effects o f im purities on m ode I crack propagation via the m olecular
dynam ics method. Tang et al. [12] generalized a previous study o f the effects o f the model
size, strain rate and tem perature on crack propagation, and the results showed that w ith the
© R. C. FENG, J. T. LU, H. Y. LI, H. CAO, Z. Y. RUI, 2017
ISSN 0556-Î7ÎX. Проблемы прочности, 2017, N2 1 87
mailto:Lujiant@163.com
R. C. Feng, J. T. Lu, H. Y. Li, et al.
increase o f the m odel, the y ield stress decreases, in addition to the m inim al model. Strain
rate and tem perature increase also reduce the y ield stress, while the elastic m odulus is not
affected. Researchers [13-15] studied the effect o f tem perature on crack propagation.
The above studies w ere focused on the effect o f strain rate, tem perature and the shape
o f crack on crack propagation. However, the existing crack m odes can vary, as w ell as the
angles betw een m icrocracks and loading direction. Therefore, the effects o f the angle
betw een m icrocrack and the loading direction on crack propagation are investigated in this
paper, and the angle o f 0, 45, and 90° are chosen to study the m echanical properties o f
single-crystal y-TiAl alloys. The m odel is show n in Fig. 1.
Fig. 1. Schematic diagram of the model with various crack inclination angles: 0 (a), 45 (b), and 90° (c).
1. M ethod . y-TiAl alloy has face-center tetragonal (FCT) structure w ith L10 structure,
as shown in Fig. 2 [16]. The crystal orientation [100], [010], and [001] corresponds to x, y,
and z axes, respectively.
Fig. 2. Atomic configurations of y-TiAl unit cell.
To observe the crack propagation behavior, the m odel that contains as m any atoms as
possible. To avoid excessive calculation, the m odel should be not too large. Therefore, the
size o f the m odel is 100aX 45aX10c, where a = 0.405 nm and c /a = 1.045. The initial
pre-crack w as introduced by rem oving the atoms. The initial crack length is 4a . To achieve
plane strain condition, the periodic boundary condition w as assigned in the z direction.
The border atomic layers o f y direction were fixed by LAM M PS [17] program m ing
method. W ith the purpose o f elim inate the stress oscillation, the loading w as carried out by
applying velocity along the y direction. A tom ic surface layers at the upper boundary were
fixed and applied m ode I loading. The thickness o f the atomic surface layers should be
larger than atoms cut-off distance [18]. For the sake o f alleviate the boundary effects, the
left boundary and right boundary o f the m odel were fixed.
2. P o ten tia l F u n c tio n M odel. The interatom ic potentials occupy an im portant place
in m olecular dynam ics simulations. Sun et al. [19] is perform ed to m odel crack propagation
and calculate the interatom ic potentials o f y-TiAl alloys. The total potential energy is given
e = E F i (p i ) + 1 E i j (rn ), (1)
i j* i
by 1
88 ISSN 0556-171X. npo6neMbi npouHocmu, 2017, № 1
Effect off the Microcrack Inclination Angle
where F i is the em bedded energy as a function o f the local electron density, p i is the
electron density at the atom i, p j is a pair potential interaction, and r j is the distance
betw een i and j .
3. S im ula tion Process. During equilibrium, the system tem perature is controlled by
the m ethod o f rescaling the atom velocities. The initial velocity is the M axw ell-B oltzm ann
distribution. Energy m inim ization and conjugate gradient m ethod are im posed to balance
the system. D uring deformation, the system tem perature is kept at 300 K using the
N ose-H oover therm ostat in the N PT ensemble applied to the system during the loading
process. A tom ic trajectory is calculated v ia velocity - Verlet integration algorithm method.
The com m on neighbor analysis (CNA) m ethod [20] is used to highlight the defects, such as
dislocations, stacking faults, and tw inning [21]. A tom ic configurations are visualized by
OVITO [22].
4. R esults an d Discussion. W hen the inclination angle is 0°, during elastic deformation,
w ithout the consideration o f the m aterial elongation along the y direction, it can be found
that the crystal structure has been not changed. This im plies that the lattice bears external
forces by changing the distance betw een atoms in the crystal structure rather than changing
the crystal structure in the initial tensile stage. A t the moment, the stress concentration
occurs at two crack surfaces. W ith the increasing strain, the atoms o f the crack surfaces
present an out-of-order state. The atoms are out o f the ideal position. A fter the integrity o f
the crystal is violated, the m odel presents an am orphous state. Chaotic arrangem ent o f the
atoms results in 1/6 <112> Shockley dislocations and 1/2 <110> full dislocations nucleation.
A s the energy is further increased, once m ore than the Peierls barrier, the dislocations will
be emitted. The first dislocation is em itted at t = 86 ps. The atomic lattice rearranges, and
strain energy is released. M oreover, a disordered region is form ed around the crack tip,
w hich includes 1/6 <112> partial dislocations, 1/2 <110> full dislocations and 1/6 <110>
stair-rod dislocations. Then the m aterial undergoes plastic deformation, w hile dislocations
are hindered by lattice resistance and slip along (111) plane. The phenom enon is consistent
w ith the theoretical explanation that the distance is the longest in the close-packed plane
and the interatom ic force is the weakest. Due to boundary im age force, dislocations slip
tow ards the boundary. As the load is further increased, m ore atomic bonds get broken and
recom bined. The disordered regions becom e large. The crack extends by m eans o f driving
the disordered regions. D uring crack propagation, there are dislocations nucleation and
em ission in the disordered region. The dislocation slips destroy the regular stacking
sequence o f partial crystal atoms. The m icrostructure o f crack tip indicates that w hen
t = 86 ps, there are the tw o-layer intrinsic stacking faults w ith HCP structure along (111)
plane and (111) plane formed, as shown in Fig. 3a. Figure 3b shows atomic configurations
at t = 94 ps. It can be found that the stacking faults propagate along two close-packed
surfaces. It is obvious that the growth rate along the (111) plane is higher than along the
(111 ) plane. W hen the stacking faults propagate along (111 ) plane, partial dislocations 1/6
[21 1] and 1/6 [ 121] are com bined into 1/6 [110] stair-rod dislocation since they slip along
the different plane, as can be seen from Fig. 4. It is com m only know n as Lom er-C ottrell
lock [23], w hich can improve the strength to some extent.
W ith the expansion o f the stacking faults, the void is form ed at t = 97 ps because of
the fracture o f atomic bonds. As the plastic deform ation is further increased, the separation
o f atoms is enlarged and gradually forms vacancy. Finally, vacancies evolve into void. As
strain is increased, the void form ed the subcrack. A t the moment, 1/6 [110] stair-rod
dislocations disappear. The subcrack breaks away from m ain crack and forms the new
crack tip. Then the subcrack begins to propagate tow ard the sm aller stress concentration
region.
A lthough the loading is hom ogeneous, the Brownian m otion is random. So the crack
extends straight along the [100] direction, then along the [ 100] direction. The void appears
at the crack tip at t = 103 ps, then evolves into the subcrack. During the subcrack
ISSN 0556-171X. npodneubi 2017, N2 1 89
R. C. Feng, J. T. Lu, H. Y. Li, et al.
a b
Fig. 3. Atomic configurations for the crack inclination angle 0° at différent time instants: (a) t = 86 ps;
(b) t = 94 ps.
Fig. 4. The Lomer-Cottrell lock.
Fig. 5. Stacking fault tetrahedra. Fig. 6. Z-shaped stacking fault.
propagates, stacking fault tetrahedron (SFT) is formed, as can be seen from Fig. 5. The
edges o f the tetrahedron are com posed o f stair-rod dislocations. The surfaces o f the
tetrahedron are com posed o f stacking faults. There is the Z -shaped stacking fault form ed
at the subcrack tip, as can be seen from Fig. 6. The m aterial is fully broken dow n at
t = 292 ps. A large num ber o f dislocations and stacking faults disappear from crack [24].
However, Z -shaped stacking fault does not com pletely disappear.
During crack propagation, 1/6 [211] and 1/6 [211] partial dislocation are com bined
into a new partial dislocation 1/3 [001], com m only know n as the H irth lock [25]. The
stability o f the dislocations is worse than 1/6 [110] dislocations.
Figure 7 depicts the atomic configurations at different tim es w hen the angle is 45°.
Because o f the discontinuity o f the geometry, the stress concentration appears at the crack
tip. A t t = 66 ps, the first dislocation is em itted from the crack tip, w hich results in the
disordered structure at the crack tip. Therefore, a dislocation-free zone is form ed in the
front o f the crack tip. As dislocations slip tow ard the boundary along the close-packed
plane (111), the tw o-layer intrinsic stacking fault along the (111) plane is form ed at the left
crack tip. Observing the atomic configurations at t = 77 ps finds that the stacking fault
90 ISSN 0556-171X. npoôëeubi 2017, N2 1
Effect o f the Microcrack Inclination Angle
propagates along the (111) plane. W ith the crack propagating tow ard the left, the stacking
faults gradually disappear. During crack propagation, the dislocations are piled up in the
boundary and form a new dislocation source. W hen the dislocations em itted from the new
dislocation source begin to slip, the tw o-layer intrinsic stacking faults are form ed along the
(111 ) plane. A t t = 82 ps, the tw o-layer intrinsic stacking faults along the (111) plane are
formed at the right crack tip. The stacking faults propagate along the (111) plane at t = 93 ps.
A s the crack propagates tow ard the right, the stacking faults gradually disappear. The void
is form ed because o f disordered structure in dislocation-free zone. The void evolves into
the subcrack. Eventually it converges w ith the m ain crack, then forms a new m ain crack.
Then the new subcrack propagates and converges w ith the new m ain crack. N am ely the
crack propagates by means o f the mechanism o f sub-main crack propagation. A t t = 158 ps,
the m aterial is fully broken down. Com pared w ith 0°, the num ber o f stacking faults and
dislocations significantly decreases in the crystal. During the whole crack propagation,
there are fewer H irth and Lom er-C ottrell locks formed.
c d
Fig. 7. Atomic configurations for the crack inclination angle 45° at different time instants: (a) t = 70 ps;
(b) t = 77 ps; (c) t = 82 ps; (d) t = 93 ps.
Figure 8 illustrate the atomic configurations at different tim es w hen the angle is 90°.
The first dislocation is em itted from crack tip at t = 63 ps. A dislocation-free zone is
form ed in the front o f the crack tip. The crack propagates by m eans o f driving the
dislocation-free zone. The w ay o f crack propagation is identical w ith the angle 45°. A t
t = 7 9 ps, the tw o-layer intrinsic stacking faults along the (1 1 1 )p la n e and the (11 1 ) plane
are form ed at the crack tip. The stacking faults propagate along the (111 ) plane and the
(111 ) plane. A s the crack propagates tow ard the left, the stacking faults disappear from the
new subcrack. W hen the crack propagates tow ard the right, the dislocations are piled up in
the low er right boundary, w hich results in the form ation o f the new dislocation source.
W hen the dislocations are em itted from the new dislocation source and glide, the tw o-layer
intrinsic stacking faults are form ed along the (111) plane. As the crack further propagates
tow ard the right, the dislocations are piled up in the upper right boundary, w hich results in
the form ation o f the new dislocation source. W hen the dislocations glide from the
dislocation source, the tw o-layer intrinsic stacking faults are form ed along the (111 ) plane.
A t t = 150 ps, the m aterial is fully broken down. A t the m om ent, there are only a small
ISSN 0556-171X. npoôëeubi 2017, N2 1 91
R. C. Feng, J. T. Lu, H. Y. Li, et al.
Fig. 8. Atomic configurations for the crack inclination angle 90° at different time instants: (a) t = 79 ps;
(b) t = 82 ps; (c) t = 93 ps; (d) t = 121 ps.
num ber o f dislocations w ithout stacking fault in the crystal. During the whole crack
propagation, the num ber o f H irth locks and Lom er-C ottrell ones is far less than 0° and is
identical w ith 45°.
A s for the different angle betw een m icrocrack and loading direction, the stress-strain
curves for crack propagation are plotted in Fig. 9. During the elastic deform ation stage, the
stress-strain curves are overlapped. The stresses increase alm ost linearly. The phenom enon
is consistent w ith the Hooke law. It also im plied that the elastic m odulus is not affected by
the angle. As the angles increase from 0 to 90°, the critical stress decreases from 9.36 GPa
at 0° to 8.13 G Pa at 45°, and then drops from 8.13 G Pa at 45° to 7.91 G Pa at 90°. The drop
in yield stress shows that the critical stress for dislocation nucleation decreases w ith the
angle. It also indicates that the angle effect on crack propagation w eakens w ith the angle.
Fig. 9. Stress-strain relations for different crack inclination angles.
92 ISSN 0556-171X. npoôëeubi npouuocmu, 2017, N2 1
Effect o f the Microcrack Inclination Angle
As strain is further increased, the atomic bond is broken down, the stress is released.
The drop in stress indicates that the m aterial begins to enter the plastic deformation.
Primarily, the m odel w ith the angle 90° enters, following w ith 45°. Finally, the m odel w ith
the angle 0° enters. The stress for the angle 45° drops to zero im m ediately after yielding,
im plying that the fracture is brittle. A s for 0 and 90°, the stress decreases due to the rupture
o f atomic bond and increases again due to the form ation o f the new bond in the plastic
deformation. Thus the stress vibrates in the stress-stra in curve. Once the rate o f the rupture
o f atomic bond exceeds the rate o f form ation o f the new bond, the stress drops sharply until
the final fracture.
C onclusions. In this study, m olecular dynam ics m ethod is em ployed to m odel crack
growth and investigate the m echanical properties o f single-crystal y-TiAl alloy when
adopting different angle betw een m icrocrack and loading direction. A ccording to the above
analysis, the following conclusions are obtained.
1.Different angle values im ply different tim e periods required for the first dislocation
emission: larger angles correspond to shorter tim e periods. W hen the dislocations slip along
the close-packed plane, intrinsic stacking faults, the H irth and Lom er-C ottrell locks are
formed, and as the angle increases, the their num ber decreases. In addition, the stacking
fault tetrahedral appears only in the m odel w ith 0°.
2. W ith the crack expansion, fracture firstly occurs at the angle is 90°, and finally
occurs at 0°.
3. The crack inclination angle has a significant influence on the crack propagation
behavior. W ith the angle increase, the critical stress drops from 9.36 to 7.91 GPa, while the
ultim ate strain is also reduced from 9.4 to 6.93%.
A cknow ledgm ents. This w ork was financially supported by N ational N atural Science
Foundation o f G ansu Province, China (No. 148RJZA008), Research project o f Gansu
Province, China (No. 2014A-033) and D octoral research fundation o f Lanzhou U niversity
o f Technology. Feng Ruicheng would like to thank Key Laboratory o f Digital Manufacturing
Technology and Application, the M inistry o f Education, Lanzhou University o f Technology
for providing help.
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