вход по аккаунту



код для вставкиСкачать
Ceramics International xxx (xxxx) xxx–xxx
Contents lists available at ScienceDirect
Ceramics International
journal homepage:
Numerical simulation and experimental study on crack self-healing in BK7
Chu Wanga, Hongxiang Wanga, , Lu Shena, Jing Houa,b, Qiao Xub, Jian Wangb, Xianhua Chenb
School of Mechatronics Engineering, Harbin Institute of Technology, Harbin 150001, China
Research Center of Laser Fusion, China Academy of Engineering Physics, Mianyang 621900, China
Surface crack
Numerical simulation
Prediction model
Crack self-healing is the result of a combination of multiple effects and involves many factors, such as mechanics,
thermodynamics, physics, and chemistry. In this paper, a finite element simulation model and a modified cracklength-prediction model for crack self-healing in BK7 glass were proposed and verified experimentally. The
simulation results showed a stress concentration at the tip of the crack at the initial stage of the crack self-healing
process. The crack length decreased gradually, and the stress concentration area moved to the surface. The stress
concentration area almost disappeared when the crack was healed completely. When the relative humidity was
64% and the compression was 5 MPa, under variable-temperature heating, the required time for a 19.8 µm precrack complete healing was 7.5 h. As the temperature increased, the required time for complete healing decreased, the contact state between the crack boundaries was improved, and thus the cracks were connected and
1. Introduction
During the grinding, polishing, and finishing of brittle optical elements, defects such as breakages, scratches, cracks, dislocations, residual stresses, and impurities are generated in the material surface or
subsurface [1]. These defects are precursors of laser damage to optical
elements, and initial laser damage points are often formed in their vicinity [2]. Under high-power laser irradiation, the initial laser damage
points of the optical elements are tens of microns, and the size of the
damage increases exponentially with laser fluence [3]. To improve the
laser-induced damage threshold (LIDT) of optical elements, pretreatment is attempted before use. The main pretreatment methods include
chemical etching [4], ultraviolet and carbon dioxide laser irradiation
[5,6], ion-beam polishing [7], MRF polishing [8], and high-temperature
annealing [9]. Although these pretreatment methods have their own
advantages, they exhibit some limitations. It is necessary to find a new
pretreatment method to improve the LIDT of optical elements.
When brittle material anneals under appropriate conditions (temperature, humidity, pressure, and residual stress), material in the
complex physical and chemical reactions will produce phenomena,
such as softening, viscous flow, blunt crack tips, and crack self-healing,
and these can mitigate crack [10–13]. Theoretically, this method improves the LIDT of optical elements used in high laser fluence. However, crack self-healing is not only crack closure, disappearance, or the
recovery of material strength. The temperature, pressure, humidity and
heat-treatment time need to be controlled accurately during the process. If the treatment transforms the material from the glass to the
molten state, the surface roughness and shape error of the optical elements will be influenced, which results in the destruction of optical
The temperature, pressure, and humidity are important external
factors that affect the solid-phase reaction. Many scholars have conducted research on the influence of these factors on crack self-healing.
Zhu et al. investigated the crack healing behavior of (MoNb)Si2 materials with high-temperature oxidation in air. The material bending
strength recovered significantly after heat treatment and the crackhealed samples exhibited higher bending strengths than the original
level after treating in 1200 °C [14]. Doquet et al. found partial crack
healing after annealing in air at 425 °C when a 20-MPa compressive
stress was applied, and annealing at 450 °C under 20 MPa pressure led
to a complete disappearance of the crack. The results also show that a
high compressive stress can shorten the crack and promote healing
[15]. Nam et al. investigated the crack healing behavior of SiC ceramics. The heat-treatment temperature has a significant influence on the
healing process, and the optimum temperature for SiC healing is
1100 °C [16]. Xu et al. found that the effect of increasing the pressure of
heating at low temperature was not obvious, and an unbalanced pressure can increase the time for complete healing [17].
Corresponding author.
E-mail address: (H. Wang).
Received 8 September 2017; Received in revised form 18 October 2017; Accepted 18 October 2017
0272-8842/ © 2017 Elsevier Ltd and Techna Group S.r.l. All rights reserved.
Please cite this article as: Wang, C., Ceramics International (2017),
Ceramics International xxx (xxxx) xxx–xxx
C. Wang et al.
Fig. 1. Sample preparation process.
response, and to enable the self-healing method to be used in optical
engineering, we need a finite element method model of the healing
process that considers the influence of multiple physical fields and
covers the entire framework.
BK7 glass material was used as the object of the research. Based on
the creep characteristics of BK7 glass at a high temperature and the
constitutive model of different creep stages, a finite element simulation
model for crack self-healing was proposed and established. The influence of temperature and time on the healing process was analyzed.
Finally, the feasibility and the correctness of the model were verified
These investigations indicate that reaction and diffusion can be
enhanced by an increase in temperature, and a high temperature with
hot pressing can improve the contact state between crack boundaries
and shorten the cracks significantly. Transmission between the same
materials can cause crack healing and a restoration of material strength
[14–17]. The glass viscosity is dependent on the temperature and water
content. When a small amount of water is introduced into the melt
glass, the material viscosity around the crack can be reduced by water
dispersion and glass hydrolysis. Viscous creep flow causes crack healing
and the recovery of material strength, and it blunts cracks, which mitigates the stress concentration at the crack tip, which improves the
LIDT. However, cracks heal only when the temperature approaches the
softening temperature (Ts), and the softening temperature is only tens
of degrees lower than the glass transition temperature (Tg), so the
temperature control must be very precise during the heat treatment
The finite element method is used to simulate crack self-healing,
and the simulation results are intuitive with a low cost. Therefore, many
scholars have tried to improve simulations of crack self-healing. Nielsen
et al. developed and validated a three-dimensional model to simulate
glass tempering, assembled from models of temperature-dependent
viscoelasticity and structural relaxation. A prediction of transient and
steady-state stresses in complex three-dimensional glass geometries was
achieved, and convergence analysis and experimental verification were
carried out [18]. Barth et al. used the finite element code Abaqus to
simulate cooling of a bulk borosilicate glass. The influence of thermal
gradient on the stress concentration and solidification process was
analyzed. The dissipation of thermal strain during the transition from
liquid to solid reduced the cracking phenomenon during cooling [19].
Nielsen, Barth et al. provided new ideas and reference data for the crack
healing of brittle materials. Xu et al. used Abaqus to simulate SCN-1
glass crack closure and healing. The influence of stress, temperature,
and crack morphology on the healing behavior of the glass were investigated and discussed. With an increase in temperature, the increased creep deformation and the grain diffusion promoted crack
closure and healing [17]. Doquet et al. used the finite element method
to simulate the effect of different constraints on the crack healing of
inert borosilicate glass. The crack boundary was shortened with an
increase in pressure at 400 °C annealing, and eventually the boundary
was connected and healed. The tensile strength of the bridging layers
was estimated to be 27–39 MPa after vacuum annealing at 400 °C [15].
These results indicate that crack self-healing involves many factors,
such as mechanics, thermodynamics, physics, and chemistry, and is the
result of multiple effects. Although different models have been proposed to analyze the crack variation at different stages during the
healing process, it cannot be expressed by a single mechanism, and the
results of a single crack model cannot be generalized to multiple cracks
by simple linear superposition. Moreover, local variation at the crack
boundary is usually unsynchronized and disordered, the crack healing
path is unpredictable, and irregular secondary cracks are also involved
[17]. To match the healing behavior of a single crack with the macro
2. Sample preparation
BK7 glass surface microstructures that were introduced by grinding
were observed through cross-sectional microscopy detection technology. [20] The surface crack morphologies were observed by atomic
force microscopy (Nanite B, Nanosurf Ltd. contact mode, lateral resolution of 1.7 nm, axial resolution of 0.34 nm, and scanning area of
110 µm × 110 µm × 22 µm). The concrete steps were as follows:
(1) Two sides of the BK7 glass (30 mm × 15 mm × 6 mm) were
polished (the CeO2 particle diameter was 1.5 µm, the polishing solution
concentration was 8 wt%, the polishing time was 4 h). (2) The two
polished surface were bonded by melting paraffin, and the two parts
were clamped by using a vice to provide a uniform and thin adhesivelayer thickness to prevent breakage during polishing, then the sample
was placed at room temperature until the paraffin cooled. The principle
is shown in Fig. 1. (3) The up-surface was lapped by using SiC of W28,
with a lapping time of 1 h, and a lapping-fluid concentration of 8 wt%.
(4) The BK7 glass was immersed in hot water to melt the paraffin, and
was placed in an ultrasonic cleaner to remove impurities. The cleaned
components were placed into a mixed solution (1.5% hydrofluoric acid
and 1.5% NH4F) for 30 s to remove the hydrolysis layer for crack exposure and then cleaned again by ultrasonic cleaner. (5) The crosssectional morphology was studied by atomic force microscopy. The
surface-crack morphologies and distribution were obtained.
Two obvious cracks on two specimens were selected for further simulation and heating experiments. The length of the first crack was
19.8 µm, its inclination angle was 85.1°, and its maximum crack width
was 235 nm (Fig. 2(a)). The length of the other crack was 26.5 µm, its
inclination angle was 86.8°, and its maximum width was 330 nm
(Fig. 2(b)).
3. Heat healing experimental procedures and results
A heating experiment was carried out to verify the feasibility of the
simulation method under variable-temperature heating conditions, and
the morphologies of the BK7 glass surface cracks were obtained by
optical microscopy.
The cracked sample (length of 19.8 µm) was heated in five steps
under a 5-MPa pressure and at a 64% relative humidity in a vacuum
Ceramics International xxx (xxxx) xxx–xxx
C. Wang et al.
Fig. 2. Section profiles of the two cracks.
Fig. 3. Procedures in variable-temperature heating experiment.
Fig. 4. Morphologies of crack healing under variable-temperature heating.
In Figs. 4 and 5, the crack length of two surface cracks (lengths of
19.8 µm and 26.5 µm) under a particular compressive stress (5 MPa)
and humidity (64% relative humidity) decreased with an increase in
heat-treatment temperature and time, and the crack disappeared completely eventually. This result indicates that water can improve the
contact state between the crack boundaries and shorten the crack. The
material viscosity decreased with an increase in temperature and water
diffusion, the viscous flow caused the crack length to decrease gradually, and finally the cracks were healed.
heating furnace. The process and parameters of the heating experiment
are shown in Fig. 3. The morphologies and distribution of the surface
cracks after each heating were observed by optical microscopy, and the
images are shown in Fig. 4.
We investigated the heat-healing process under constant temperature. The second crack (length of 26.5 µm) was heated in 5 steps
(500 °C, compression of 5 MPa, 64% relative humidity, the heating time
of each step was 1 h, and cooling was at room temperature for 10 h).
The crack morphologies after each heating step are shown in Fig. 5.
Ceramics International xxx (xxxx) xxx–xxx
C. Wang et al.
Fig. 5. Morphologies of crack healing under constant-temperature heating.
Fig. 6. Variations of creep strain of glass material at different times.
Table 1
BK7 glass parameters.
Elastic modulus E (MPa)
Poisson's ratio μ
Thermal expansion coefficient α (/K)
Qc (kJ/mol)
Fig. 7. Finite element model with a V-type edge crack.
stable creep stage in which the strain rate remains constant, and the
third is the accelerating creep stage in which the strain rate increases
with time [21].
The creep equation of BK7 glass is expressed by the creep strain rate
4. Numerical simulation of crack self-healing
4.1. Constitutive model
ε ̇ ∝ f (T )⋅f (σ )⋅f (S )
Brittle glass material that is heated at a certain stress and high
temperature will produce creep, and the creep process is divided into
three stages, as shown in Fig. 6. The first stage is the deceleration creep
stage in which the strain rate decreases with time, the second is the
where ε ,̇ T, σ , and S are the creep strain rate, temperature, compression
stress, and structure factor, respectively, which characterize the effects
of density, porosity, and other internal structures on the creep strain
Ceramics International xxx (xxxx) xxx–xxx
C. Wang et al.
Fig. 8. Stress distributions after each heating step in variable-temperature simulation.
compression stress (MPa), n is the average stress index, Qc is the average
apparent activation energy (kJ/mol), R is the gas constant, T is the
absolute temperature (K), and A exp(−Qc / RT ) describes the BK7 glass
viscosity dependence on temperature.
The creep of BK7 glass at high temperature is determined by temperature and compression, and the internal material structure changes
The creep strain rate in the stable creep stage can be described as
εċ st = Aσ n exp(−Qc / RT )
εċ st
is the creep strain rate, A is the material constant, σ is the
Ceramics International xxx (xxxx) xxx–xxx
C. Wang et al.
Fig. 9. Stress distributions in constant-temperature heating simulation.
significantly when it is near the transition temperature (Tg). This
change influences the creep strain rate of the stable creep stage.
Therefore, we need to correct Eq. (2) to a modified equation [26]:
where (T / Tg ) γc describes the effect of temperature near Tg on the creep
strain rate and γc is the index of structure in the stable creep stage.
The constitutive equation of BK7 glass in the stable creep stage is
obtained by integrating time:
εċ st = Aσ n exp(−Qc / RT )(T / Tg ) γc
εcst (σ , T , t ) = Btσ n exp(−Qc / RT )(T / Tg ) γc
Ceramics International xxx (xxxx) xxx–xxx
C. Wang et al.
obtained previously (length of 19.8 µm, inclination angle of 85.1°, and
maximum width of 235 nm). The simulation pressure was set to 5 MPa;
the heating process was divided in 5 steps; the heating temperatures
were 400 °C, 425 °C, 450 °C, 475 °C, and 500 °C; and the time for each
heating step was 1.5 h. The stress distributions after each heating step
in the simulation are shown in Fig. 8.
A simulation under constant temperature was also carried out. The
model dimensions were set as the second crack we obtained previously
(length of 26.5 µm, inclination angle of 86.8°, and maximum width of
330 nm). The same model was heated at the same temperature but for a
different heating time. The heat-healing simulation parameters were as
follows: the pressure was 5 MPa; the heating temperature was 500 °C;
and the heating times were 1 h, 2 h, 3 h, 4 h, and 5 h, respectively. The
stress distributions in the simulation for different heating times are
shown in Fig. 9.
Table 2
Calculation results for slope k.
Experiment number
P (MPa)
T (°C)
where B is the material constant.
In the deceleration creep stage, the creep strain rate decreases with
time, and finally tends to stability. The process is short, and the constitutive equation is expressed as:
εcin (σ , T , t ) = A (1 − exp(−kt )) σ n exp(−Qc /RT )(T /Tg ) γc
5. Prediction model of crack-healing length
Greil proposed a model of the crack length with time at a given
temperature and pressure [27]. When a pressure is applied to the specimen under constant-temperature conditions, crack healing is accelerated. After a given time, the crack length can be predicted by the
following formula:
where k is the material constant and t is the time.
The constitutive equation of the total creep process of BK7 glass at
high temperature can be obtained by combining Eqs. (4) and (5) as:
εc (σ , T , t ) = σ n exp(−Qc /RT )(T /Tg ) γc⋅[A (1 − exp(−kt )) + Bt ]
cheal = cdam − Fσ mt
where cheal is the crack length after heating, cdam is the crack length
before heating, t is the heating time, F and m are constants that describe
the crack healing of the material at a certain temperature and stress, F
varies from 0 to 1, m varied from 0 to 4, σ is the stress, and Fσm can
describe the healing rate under certain conditions.
However, F and the m are not the same at different temperatures,
and the formula does not give direct correspondence between these two
parameters and the temperature. Therefore, we cannot use the formula
proposed by Greil to calculate the crack length.
Through our finite element simulation of the crack-healing process,
combined with the experimental design and regression analysis, the
slope of the curve of crack length change with time at a certain temperature and pressure can be obtained. The experimental design and
calculation results are shown in Table 2, and the slope of the curve can
be given by:
4.2. Material parameters and boundary conditions
BK7 glass is a typical hard and brittle material with parameters as
shown in Table 1. To investigate the influence of compression and
temperature on the BK7 glass healing process, it is necessary to exert
pressure on the surface of the element (shown in Fig. 5) and to apply a
temperature field to the model. Because the sample was small, and the
heat-transfer effect was very rapid, the entire model was set at the
heating temperature. All degrees of freedom of the right surface in the
model were constrained to prevent movement and rotation during the
simulation. When the two sides of the crack make contact, the crack is
defined as healed. The variation in crack length with time and the
complete healing time can be obtained by real-time monitoring of the
k = 44.95576 + 2.027267P − 0.24593T − 0.00348PT − 0.01426P 2
4.3. Numerical simulation
+ 0.000327T 2
It is necessary to establish the crack geometric model according to
the actual size for the simulation. A two-dimensional planar model
(0.5 mm × 0.5 mm) was established by using the finite element code
A simulation of heating at variable temperature was carried out. The
model dimensions (Fig. 7) were set according to the first crack that we
where k is the slope of the curve, P is the pressure (MPa), and T is the
temperature (°C).
An improved crack-length prediction model during healing can be
obtained from:
cheal = cdam − kt
Fig. 10. Variations in crack length obtained experimentally and by prediction (a) under variable-temperature heating and (b) under constant-temperature heating.
Ceramics International xxx (xxxx) xxx–xxx
C. Wang et al.
Fig. 11. Relationships of crack length with time (a) for different pre-crack lengths, pressures of 5 MPa, and a heating temperature of 500 °C; (b) for different temperatures, a pressure of
5 MPa, and a crack length of 20 µm; (c) for different pressures, a heating temperature of 500 °C and a pre-crack length of 20 µm.
brittle materials. As the temperature increases, the viscosity decreases
rapidly and viscous flow is accelerated, therefore, the time for complete
healing is reduced. However, when the temperature exceeds the glasstransition temperature (556 °C), the internal structure of the glass material will change from the glass to the molten state, which will affect
the optical element surface accuracy and roughness directly. Fig. 11(c)
shows that the time was reduced significantly when the pressure exceeded 5 MPa. This occurs because the applied pressure can counteract
the residual tensile stress that is caused by grinding and/or polishing
and reduce the crack width simultaneously, which promotes viscous
flow. When the pressure is too large or exceeds the material strength
limit, the glass will break with more cracks, and produce permanent
plastic deformation. Therefore, the pressure that is applied should be
limited, so that crack healing can be more efficient and prevent additional damage and plastic deformation.
Under a given temperature and pressure condition, the crack length
at any time can be calculated directly by using Eq. (9). For the cracks
that we selected previously (length of 19.8 µm and 26.5 µm), variations
in crack length under variable and constant temperature can be obtained (Fig. 10).
By using Eq. (9), we can obtain the required time for complete
healing of cracks of different lengths, and the results are shown in
Fig. 11(a). Similarly, variations in crack length with time under a 5MPa pressure and various heating temperatures can be obtained
(Fig. 11(b)). The variations in crack length with time are shown in
Fig. 11(c) at 500 °C and 2.5 MPa, 5 MPa, 7.5 MPa, 10 MPa, and
12.5 MPa.
6. Results and discussion
In Figs. 8 and 9, an obvious stress concentration exists at the tip of
the crack. The crack was filled by material viscous flow, and the crack
length and width were reduced gradually. At the same time, the stress
concentration area moved gradually to the left surface of the model.
When the crack is healed completely, the stress concentration area almost disappears.
Fig. 10 shows that the experimental results and prediction model
are in good agreement, which verifies the correctness of the proposed
prediction model.
From Fig. 11(a), the healing rate of cracks of different lengths was
the same under certain pressure and temperature conditions, and the
length was linear with time. When the pressure was constant, a higher
temperature yielded a higher healing rate and a lower time for the same
crack length to heal completely, which agrees with the thermodynamic
theory above. Fig. 11(b) shows that the required time for complete
healing decreased with temperature. This occurs because the crackhealing reaction needs to overcome the activation barrier by reaching a
certain temperature, and the temperature influences the viscosity of
7. Conclusions
A finite element simulation of BK7 glass crack self-healing was
proposed and the process was simulated numerically. The effect of
temperature on crack healing was analyzed, and the correctness and
feasibility of the simulation model were verified experimentally.
The simulation results show an obvious stress concentration at the
tip of the crack at the initial stages of crack healing. With crack healing,
the length and width of the crack were reduced gradually, and the stress
concentration area moved gradually to the left surface of the model.
Finally, the crack was healed completely, and the stress concentration
area almost disappeared.
An improved crack-length prediction model was proposed and
verified experimentally. The influences of crack length, temperature,
and pressure on the crack healing rate were analyzed. Under different
pressure and temperature conditions, the healing rate was the same for
a different crack length, and the healing length was linear with time.
Ceramics International xxx (xxxx) xxx–xxx
C. Wang et al.
Laboratory (LLNL), Livermore, CA, 2006.
[9] Y. Jiang, X. Xiang, C. Liu, H. Wang, W. Liao, H. Lv, X. Yuan, R. Qiu, Y. Yang,
W. Zheng, Effect of residual stress on laser-induced damage characterization of
mitigated damage sites in fused silica, J. Non-Cryst. Solids 410 (2015) 88–95.
[10] K. Ando, M.-C. Chu, K. Tsuji, T. Hirasawa, Y. Kobayashi, S. Sato, Crack healing
behaviour and high-temperature strength of mullite/SiC composite ceramics, J. Eur.
Ceram. Soc. 22 (8) (2002) 1313–1319.
[11] X.-P. Zhang, J.-H. Ouyang, Z.-G. Liu, Y.-J. Wang, Y.-M. Wang, Y. Zhou, Crackhealing ability and strength recovery of different hot-pressed TZ3Y20A–SiC ceramics by heat treatment in air, Mater. Des. 67 (2015) 324–329.
[12] K. Houjou, K. Ando, S.-P. Liu, S. Sato, Crack-healing and oxidation behavior of
silicon nitride ceramics, J. Eur. Ceram. Soc. 24 (8) (2004) 2329–2338.
[13] R. Singh, S. Parihar, Self Heallng behavior of glasses for high temperature seals in
solid oxide fuel cells, Adv. Solid Oxide Fuel Cells III: Ceram. Eng. Sci. Proc. 28 (4)
(2009) 325–333.
[14] G. Zhu, X. Wang, Q. Lu, G. Wu, P. Feng, High-temperature crack-healing behaviour
and strength recovery of (MoNb) Si 2, Appl. Surf. Sci. 343 (2015) 41–48.
[15] V. Doquet, N.B. Ali, E. Chabert, F. Bouyer, Experimental and numerical study of
crack healing in a nuclear glass, Mech. Mater. 80 (2015) 145–162.
[16] K.W. Nam, J.S. Kim, Critical crack size of healing possibility of SiC ceramics, Mater.
Sci. Eng.: A 527 (13) (2010) 3236–3239.
[17] W. Xu, X. Sun, E. Stephens, I. Mastorakos, M.A. Khaleel, H. Zbib, A mechanisticbased healing model for self-healing glass seals used in solid oxide fuel cells, J.
Power Sources 218 (2012) 445–454.
[18] J.H. Nielsen, J.F. Olesen, P.N. Poulsen, H. Stang, Finite element implementation of a
glass tempering model in three dimensions, Comput. Struct. 88 (17) (2010)
[19] N. Barth, D. George, S. Ahzi, Y. Rémond, V. Doquet, F. Bouyer, S. Bétremieux,
Modeling and simulation of the cooling process of borosilicate glass, J. Eng. Mater.
Technol. 134 (4) (2012) 041001.
[20] Z. Wang, Study on the Detection and Control Techniques of Subsurface Damage in
Optical Fabrication (Doctoral Dissertation), National University of Defense
Technology, 2008.
[21] X. Zhao, Q. Cao, C. Wang, X. Wang, D. Zhang, S. Qu, J. Jiang, Dependence of roomtemperature nanoindentation creep behavior and shear transformation zone on the
glass transition temperature in bulk metallic glasses, J. Non-Cryst. Solids 445
(2016) 19–29.
[22] E. Heuse, G. Partridge, Creep testing of glass-ceramics, J. Mater. Sci. 9 (8) (1974)
[23] T. Rouxel, M. Huger, J. Besson, Rheological properties of Y-Si-Al-ON glasses—elastic moduli, viscosity and creep, J. Mater. Sci. 27 (1) (1992) 279–284.
[24] Ol'khovik, N. Demenchuk, Creep of organic glass under shear with superposition of
hydrostatic pressure, Strength Mater. 9 (2) (1977) 168–174.
[25] N. Smotrin, V. Chebanov, Creep of organic glass (plexiglas), Mech. Compos. Mater.
1 (4) (1965) 33–36.
[26] J. Guo, C. Yuan, H. Yang, V. Lupinc, M. Maldini, Creep-rupture behavior of a directionally solidified nickel-base superalloy, Metall. Mater. Trans. A 32 (5) (2001)
[27] P. Greil, Generic principles of crack-healing ceramics, J. Adv. Ceram. 1 (4) (2012)
The healing rate increases with temperature and pressure. When the
pressure exceeded 5 MPa, the required time for complete crack healing
was reduced significantly.
The activation energy barrier of the healing process is high, which
requires a certain temperature to activate and overcome. This occurs
because the brittle-material viscosity exhibits a viscosity-temperature
characteristic; as the temperature increases, the viscosity decreases and
the viscous flow is accelerated, so the required time is reduced. The
applied pressure is able to counteract the residual tensile stress that is
caused by grinding and polishing. As the pressure increases, the crack
boundary is shortened, and thus, the required time is also reduced.
This work was supported by the Science Challenge Project of China
(Grant No.JCKY2016212A506-0503) and National Natural Science
Foundation of China (Grant No.51475106).
[1] T. Suratwala, R. Steele, M. Feit, L. Wong, P. Miller, J. Menapace, P. Davis, Effect of
rogue particles on the sub-surface damage of fused silica during grinding/polishing,
J. Non-Cryst. Solids 354 (18) (2008) 2023–2037.
[2] P. Miller, T. Suratwala, J. Bude, T. Laurence, N. Shen, W. Steele, M. Feit, J.
Menapace, L. Wong, Laser damage precursors in fused silica, in: Laser Damage
Symposium XLI: Annual Symposium on Optical Materials for High Power Lasers,
International Society for Optics and Photonics, 2009, pp. 75040X-75040X-75014.
[3] J. Bude, P. Miller, S. Baxamusa, N. Shen, T. Laurence, W. Steele, T. Suratwala,
L. Wong, W. Carr, D. Cross, High fluence laser damage precursors and their mitigation in fused silica, Opt. Express 22 (5) (2014) 5839–5851.
[4] L. Wong, T. Suratwala, M. Feit, P. Miller, R. Steele, The effect of HF/NH 4 F etching
on the morphology of surface fractures on fused silica, J. Non-Cryst. Solids 355 (13)
(2009) 797–810.
[5] I.L. Bass, G.M. Guss, M.J. Nostrand, P. Wegner, An Improved Method of Mitigating
Laser Induced Surface Damage Growth in Fused Silica Using a Rastered, Pulsed CO2
Laser, Lawrence Livermore National Laboratory (LLNL), Livermore, CA, 2010.
[6] M.A. Stevens-Kalceff, J. Wong, Distribution of defects induced in fused silica by
ultraviolet laser pulses before and after treatment with a CO 2 laser, J. Appl. Phys.
97 (11) (2005) 113519.
[7] T. Kamimura, S. Fukumoto, R. Ono, Y. Yap, M. Yoshimura, Y. Mori, T. Sasaki,
K. Yoshida, Enhancement of CsLiB6O10 surface-damage resistance by improved
crystallinity and ion-beam etching, Opt. Lett. 27 (8) (2002) 616–618.
[8] J.A. Menapace, P.J. Davis, W.A. Steele, M.R. Hachkowski, A. Nelson, K. Xin, MRF
Applications: On the Road to Making Large-aperture Ultraviolet Laser Resistant
Continuous Phase Plates for High-power Lasers, Lawrence Livermore National
Без категории
Размер файла
1 711 Кб
ceramint, 2017, 121
Пожаловаться на содержимое документа