Open Access
Add to BibSonomy
Abstract
Precision glass molding (PGM) technology has recently emerged as a promising fabrication method for mass-fabricating optical glass lenses with complex surfaces. However, lens fracture as a common problem has not been analyzed in detail. In this paper, the divergent cone cracks in the molded lens were analyzed using the finite element method, because crack propagation cannot be seen in the molding process. A three-dimensional model was established in MSC Marc software for analyzing the temperature, stress components, and principal stress of the glass in different molding stages. The crack paths were analyzed using the simulation results and the fracture basis. Based on the analysis, PGM experiments with different processing parameters were carried out. The appearance of the molded lenses demonstrated the rationality and correctness of the analysis. Thus, analyses of other types of lens fractures can use the analysis method proposed in this paper rather than relying on trial and error.
© 2021 Optical Society of America
1. INTRODUCTION
A glass lens has advantages over a plastic lens in terms of hardness, refractive index, light permeability, and stability to environmental changes in temperature and humidity [1]. In precision glass molding (PGM), glass lenses are fabricated by compressing glass preforms between fine finished molds under highly controlled conditions to replicate the shapes of the molds in the lens surface without need for further machining processes. The whole PGM cycle can be divided into four stages: heating, forming, annealing, and cooling [2–4]. PGM technology has recently emerged as a promising fabrication method for mass-producing precision optical elements with complex shapes, like aspherical lenses, Fresnel lenses, diffractive optical elements, and microlens arrays [5–8].
The finite element method (FEM) can be applied to simulate the whole molding process due to the excellent availability of numerical simulations, the rapid development of computing technology, and the increase in task scale in data and information processing [9]. Li and Gong established an axisymmetric two-dimensional (2D) thermodynamic coupling model for predicting the residual stress and filling ratios of a large-diameter aspheric glass lens for different process parameters [10]. Due to the complexity of the Fresnel shape, the material flow in the mold was more difficult than that in a smooth aspherical lens mold. Zhou et al. simulated the material flow and the stress changes of a lens on a pressing stage, in order to optimize the molding conditions to minimize the residual stress of the formed lens [11].
Flaws in appearance, such as fractures, scratches, and bubbles, sometimes are generated on a molded lens in the process of PGM. Huang et al. indicated that in their experiments, the molded glass lens could break when the molding temperature was too low [12]. Reducing the cooling rate and operating in a vacuum environment were useful in avoiding cracks and bubbles in the lens [13]. He et al. proposed that the molded glass lens broke because of the adhesion in the experiment [14]. Zhou et al. studied the influence of the roughness and curvature of the contact surfaces, as well as the pressing force, on the formation of the micro dimples of a molded chalcogenide glass lens. The effect of the molding temperature on surface scratches was also studied [15].
Although the defects in molded lenses are occasionally mentioned, to our knowledge the fracture morphologies have not been discussed in detail. 2D finite element simulation can only reflect the stress distribution along the axial section of the lens; it is not enough for the stress analysis of a fractured lens. In this paper, the FEM software MSC Marc was used, as it is notably applicable in highly nonlinear viscoelastic analysis [16]. A three-dimensional (3D) model was established in the software to determine the distribution of the temperature and stress of the glass. Shear stress, normal stress, and principal stress were considered in the analysis of the propagation of divergent cone cracks. Based on the causal analysis, two PGM experiments were carried out. Compared to the crack morphology of the molded lens in the problem description, the predicted cracking direction was changed when the temperature setting in the heating stage was increased and the unit cycle time was extended, as shown in the first experiment. Because microcracks in the glass preform are random distributions, lens fracture is also a problem of probability. In this paper, when the probability of molded lens fracture is about 1% with a specific group of processing parameters, the parameters are recognized to be useable. Cracks were nearly completely avoided when the forming pressure was further decreased in the first forming stage, as shown in the second experiment. This study provides a method for analyzing molded lens fracture. The method may also be adapted for analyzing other types of cracks in a molded lens.
2. PROBLEM DESCRIPTION
A large number of experiments are needed to optimize the processing parameters in order to obtain the processing parameters suitable for the mass production of lenses in PGM technology. Improper parameters can lead to flaws in the appearance of the molded lenses, one of which is lens fracture. One common form of lens fracture is divergent cone cracks in the lens. It becomes important to determine which parameters are set improperly for the fabrication of such molded lenses. In one experiment, the form of lens fracture shown in Fig. 1 was often generated in the molded lens.
The glass material was M-FCD1 from HOYA Glass Inc. Both surfaces of the lens were rotationally symmetric aspherical surfaces, described by
Table 1. Coefficients of the Even Aspherical Surfaces
The fabrication of the aspheric lenses was carried out on a die transfer machine, where the tool package was transported between stations to reduce the cycle time. The machine (model ATM-ASP-8S) was from Shenzhen Aix Technology Co., Ltd., in China. The machine has eight stations, of which three are heating stations, two are forming stations, and three are cooling stations. Usually, the PGM cycle can be divided into four stages: heating, forming, annealing, and cooling. The temperature of the last station cannot be set in this machine. This station was for water cooling; the final temperature of the molds was related to the unit cycle time. The original unit cycle time was set as 65 s in this experiment. The other processing parameters were set as the values listed in Table 2. The rates of heating and cooling cannot be set, because the temperature setting values are the temperatures of the heating panels.
Table 2. Processing Parameters in the Original Experiments
3. SIMULATION MODEL
Considering the viscoelastic response of glass at the forming temperature, the FEM is helpful to analyze the stress of molded glass. A diagram of the 3D geometrical model consisting of the molds and the preform established in the finite element analysis software MSC Marc is shown in Fig. 3. In PGM technology, the factors that can lead to lens fracture include adhesion of the glass and the molds, forming temperature, cooling rate, forming pressure, and strain rate, among others. To save time, the analysis of the heating stage and the forming stage was first simulated in this section.
Fig. 3. Diagram of the geometrical model established in the finite element analysis software MSC Marc.
A. Temperature Simulation
Since the experiments were carried out with a die transfer machine, the heating of the glass preform mainly came from the molds via heat conduction. The molds and the glass preform were initially in point contact. The analysis type was defined as thermal/structural analysis. The general heat equation for the Cartesian coordinate system is
In the definition of the initial conditions, the temperature in the thermal analysis was set as 20°C for all the contact bodies. During the heating stage, the temperature of the heating panels of the PGM machine was maintained at the temperature setting value. The heating of the molds came from the heating panels via thermal conduction, as shown in Fig. 4(a). Therefore, the boundary condition of thermal analysis was to set the temperature of the nodes on the mold end face as the forming temperature. Because the central nodes of the upper mold’s lower surface, the upper and lower surfaces of the glass preform, and the lower mold’s upper surface were inconsistent with the geometric centers, heat conduction did not occur between the mold and the preform. The value of the “distance close to contact” could be set as any number greater than 0 and less than 1e-5 in the established model in this paper to ignore the small deviation between the central node positions. The value was small enough not to cause the simulation results to deviate significantly from reality. The contact heat transfer coefficient was set as ${2400}\;{\rm W}/{{\rm m}^2\,}^\circ {\rm C}$ [9]. The mold material was tungsten carbide (J05 grade). The mechanical and thermal properties of the glass preform and molds are listed in Table 3.
Table 3. Mechanical and Thermal Properties of the Glass and the Mold
To simulate the temperature of the glass when the temperature setting values were different in the heating stage, two simulations were performed. The difference between the two simulations was that one used a setting of 430°C and the other used a setting of 440°C at the mold end face nodes. The working time was set as 400 s. In recording the simulation results, each incremental step represented one second in time.
B. Stress Simulation
Thermal stress will be introduced into the glass preform when there is a temperature gradient. Thermal stress ${\sigma _{\rm th}}$ can be calculated with
Stress relaxation is one of the thermal properties of optical glass. The final minimum stress level is a function of the time, viscosity, and stress history of the glass, as expressed in the following:
where $ A $ is a constant, $ \tau $ is the relaxation time, ${\sigma _{\rm original}}$ and ${\sigma _{\rm final}}$ are respectively the original and final stress of the glass. Relaxation time is the amount of time required for the current stress to be reduced to ${{1/}}e$ of the initial stress level and is a function of the material properties and temperature [18].Due to the unavailability of the viscoelastic parameters of the M-FCD1 glass, the parameters of another glass whose viscosity is similar to M-FCD1 at the same temperature can be used for qualitative analysis. The viscosity values of the glass can be fitted to a curve by using the famous Vogel–Fulcher–Tammann equation. The thermal properties of M-FCD1 and D-ZK3L, produced by CDGM (CDGM Glass Co., Ltd., Chengdu, China), are listed in Table 4 [19]. The fitted curves of the viscosities are shown by the solid lines of different colors in Fig. 5. It is shown that the viscosity of M-FCD1 at 440°C was about 9.3 P, and D-ZK3L at 550°C was about 10.1 P. The forming stage in the PGM process usually is carried out when the glass viscosity is 7–10 P [20]. Thus, the viscoelastic parameters of the D-ZK3L glass at 550°C proposed in Ref. [21] were used in the stress simulation. The parameters are listed in Table 5. Although the stress relaxation time may be different from that of the M-FCD1 glass, it was more important to obtain the stress distribution of the glass.
Table 4. Thermal Properties of the Glasses
Table 5. Parameters of the Glass Stress Relaxation Used in the Simulation Model
In the experiment, the vertical displacement of the upper mold was controlled by the air cylinder above each station. The pressure value in the parameter setting interface was the pressure of the air cylinder. In the simulation of the forming stage, the pressure was applied to the upper mold end face, as shown in Fig. 4(b). The forming pressure includes not only the air cylinder pressure but also the gravity of the heating block. The air cylinders of the PGM machine used in this paper are double-bar air cylinders. When the inside diameter of the air cylinder is ${b_1}\; {\rm mm}$, the diameter of the piston rod is ${b_2}\; {\rm mm}$, the weight of the heating module is ${b_3}\; {\rm kg}$, the diameter of the mold end face is ${b_4}\; {\rm mm}$, the pressure is set to $ m \; {\rm MPa}$, and the forming pressure applied to the mold is $ n \; {\rm MPa}$, as shown below:
${b_1}$, ${b_2}$, ${b_3}$, and ${b_4}$ in this paper are 63, 20, 12.5, and 21, respectively. Therefore, when $ m $ equals 0.9, $ n $ equals 14.92.
The simulations in this section started with the beginning of the forming stage of PGM. When the simulation model was established, 0.1 s was set as the increment. In the established geometric model, the distance between the upper mold and the glass preform was 0.6 mm. The stress of the glass was recorded when the displacement of the upper mold was 1.015 mm; that is, the deformation of the glass was 0.415 mm. As diamond-like carbon (DLC) was used as the surface protective coating for the mold, the abrasion of the coating was not considered in this paper. Thus, the friction between the mold and the glass was not included in the stress model. The boundary conditions in the model were as follows. First, the position of the lower mold was fixed; that is, the displacement of the lower mold was set as zero. Second, the forming pressure was applied to the upper mold end face, and the value was 14.92 MPa when the air cylinder pressure was 0.9 MPa. Third, the temperature of all the nodes was set as 440°C.
The model used a right-handed coordinate system. The nine stress components in the FEM are shown in Fig. 6. The simulation results in the MSC Marc software, “comp 11 of stress,” “comp 22 of stress,” and “comp 33 of stress,” represent $ \sigma_{xx} $, $ \sigma_{yy} $, and $ \sigma_{zz} $, respectively; “comp 12 of stress,” “comp 23 of stress,” and “comp 31 of stress” represent $ \sigma_{xy} $, $ \sigma_{yz} $, and $ \sigma_{zx} $, respectively. In addition, there are the following three relationships: ${\sigma _{xy }}={\sigma _{yx}}$, ${\sigma _{yz }}={\sigma _{zy}}$, and ${\sigma _{zx }}={\sigma _{xz}}$.
4. RESULTS AND DISCUSSION
A. Fracture Basis
There are microscopic cracks larger than the distance between the atoms in each material, which reduces the overall strength of the material [22]. PGM technology is not a material removal process, so no new subsurface damage is introduced during the molding process [17]. But inevitable scratches, abrasions, microcracks, and other subsurface damage will be introduced into the glass preform when it is fabricated via material removal [23,24]. Figure 7 is a schematic diagram of the microcracks generated on the surface of a glass preform machined via material removal. The cracks are in the form of lateral, median, and chevron cracks [25,26]. Most glass preforms are processed via a material removal process.
Fig. 7. Schematic diagram of the microcracks generated on the glass preform with a material removal process.
There are three potential modes of flaw failures, denoted as mode I, mode II, and mode III, as depicted in Fig. 8. The first is an opening mode, while the others are shear modes, either sliding or tearing [22]. In the absence of external and internal stresses, glass is essentially isotropic and will not break in the preferred direction [27]. A major obstacle to its widespread use as a structural material is not its strength, but rather its generally low and highly variable fracture toughness. Fracture toughness quantifies the ability to resist catastrophic failure in the event of a crack [28]. The fracture stress of glass $ \sigma_f $ is usually just the maximum stress that is applied to the glass object at failure. The classical Griffith equation for mode I fracture is
where the term $ C $ is the flaw size at the instant of fracture in the original Griffith energy balance, $ K_{Ic} $ is the mode I critical stress intensity factor, and $ Y $ is a constant relating to the flaw geometry. Suppose that $ K_I $ is a stress field, or the so-called mode I stress intensity factor. When $ K_I $ reaches a critical value $ K_{Ic} $, spontaneous failure occurs. For mode II and mode III flaw failures, there are similar theories [22,29].The fracture strength is related to the depth and the shape of the flaw, resulting in a significant reduction in the fracture strength below the theoretical strength [30]. The measurement of fracture toughness is influenced by the surface quality and residual stress of the material [18]. Because it is difficult to control the microcracks of glass samples so that they are the same, a qualitative analysis of the cracks was carried out in this paper based on the FEM results and flaw failure modes.
B. Simulation Results and Discussion
The temperature distribution cloud map of the molds and glass when the time was 400 s is shown in Fig. 9. The temperature of the selected node in Fig. 9 in the two temperature simulations was extracted from the simulation results. The temperature–time curves of the node are plotted in Fig. 10. It can be seen that the temperatures of the selected node from the two simulations were 420°C and 410°C at 165 s. When the set forming temperature increased by 10°C, the temperature of the selected node after the heating stage increased by 10°C. This result had guiding significance for the optimization of temperature parameters. When the temperature of the selected node reached the transition temperature of the glass, the heating time was 133 s when the temperature of the boundary condition was 440°C, and 143 s when the temperature of the boundary condition was 430°C. Thus, the temperature of the glass preform was not uniform at the beginning of the forming stage. In addition, the DLC coating would make the heat transfer from the mold to the glass slower. The viscosity of optical glass at a lower temperature is greater than that at a higher temperature. Therefore, in the forming stage, deformation of the glass preform at a lower temperature will cause greater stress in the lens.
Fig. 11. Cloud maps of the (a) equivalent stress on lens surface 1 and (b) shear stress ${\sigma _{yz}}$ in the cross section.
Figure 11 shows the stress distribution of the glass at the 21st increment when the air cylinder pressure was 0.9 MPa. The automatic mesh generation of surface and solid was combined to mesh each geometry established in the FEM software in this paper. Then there was slight asymmetry among the elements. The geometry of the glass preform was divided into 20,940 elements to make the glass preform deform normally in the forming stage. Thus, the simulation results were not perfectly symmetric but would not have a negative influence on the analysis. The deformed condition of lens surface 1 and the stress component ${\sigma _{yz}}$ in the YOZ plane can be obtained in Fig. 11(a). The stress component ${\sigma _{yz}}$ is the stress on normal face $ y $, and points in the $ z $ direction. Since ${\sigma _{yz }}={\sigma _{zy}}$, the shear stress ${\sigma _{zy}}$ of the glass in the area framed by the dotted line was analyzed. Since the lens geometry was divided into a mass of infinitesimally small elements in the simulations, some small elements were together equivalent to one large element, as shown in Fig. 12. It can be seen that the glass in the two areas framed in the upper part in Fig. 11(b) was subjected to a downward force at the left and right end faces and an upward force in the middle. Similarly, the glass in the two areas framed in the lower part in Fig. 11(b) was subjected to an upward force at the left and right end faces and a downward force in the middle. Thus, once the stress intensity factor exceeded the sliding mode critical stress intensity factor, the microcracks would begin to propagate into macroscopic cracks. Because the lens was rotationally symmetric, the macroscopic crack in this situation would be a ring crack. The cracks in Fig. 1 include such a ring crack. Thus, the stress distribution provides a possible reason for the generation of the cracks in Fig. 1.
Fig. 12. Diagrams of the shear stress $ \sigma_{zy} $ of the glass in the area framed by a dotted (a) green line and (b) black line in Fig. 11(b).
The cloud maps of the stress components $ \sigma_{xx} $, $ \sigma_{yy} $, and $ \sigma_{zz} $ in the view of surface 1 in the 21st increment when the air cylinder pressure was 0.9 MPa are shown in Fig. 13. To illustrate the stress distribution more clearly, the stress cloud maps of a quarter of the glass are shown in Fig. 14. The deformation made the stress component $ \sigma_{yy} $ of the central part of the glass increase. Therefore, a ring crack on the lens surface may longitudinally propagate to a conical crack in the sliding fracture mode due to the stress component $ \sigma_{yy} $.
Fig. 13. Cloud maps of the stress components (a) ${\sigma _{xx}}$, (b) ${\sigma _{yy}}$, and (c) ${\sigma _{zz}}$ in the view of surface 1.
Fig. 14. Cloud maps of the stress components (a) ${\sigma _{xx}}$, (b) ${\sigma _{yy}}$, and (c) ${\sigma _{zz}}$ of a quarter of the glass.
Figure 15 shows the vector diagram of the maximum principal stress of the lens in the view of surface 1. The directions of the maximum principal stress were opposite each other in circumferential direction in about the outer half-diameter of the glass. The open mode of flaw failure would take place in the lens once the stress intensity factor exceeded the open mode critical stress intensity factor. This would further increase the possibility of divergent cracks occurring. Because the microcracks inside the glass preform were randomly located, the microcracks near the ring crack would randomly propagate along the radius. The final result is that the number of divergent cracks in different lenses might not be the same even if the processing parameters are the same.
At the beginning of the forming stage, the maximum absolute value of shear stress $ \sigma_{yz} $ would increase with the increasing air cylinder pressure. Thus, a ring crack would be more likely to occur in a lens with greater air cylinder pressure. The maximum absolute value of stress $ \sigma_{yy} $ also tended to increase with increasing air cylinder pressure. The stress component $ \sigma_{yy} $ made the ring crack more likely to propagate longitudinally with greater air cylinder pressure and become a conical crack.
C. Verification Experiments
According to the qualitative analysis, the unit cycle time needed to be lengthened to make the temperature of the glass uniform, and the temperature setting value should be increased to lower the viscosity of the glass preform at the beginning of the forming stage. The experiment was performed when the unit cycle was set as 100 s, and this was numbered as experiment No. 1. Other processing parameters are listed in Table 6. One of the molded lenses fabricated with this group of parameters had the appearance shown in Fig. 16. It is seen that the diameter of the ring crack is bigger than that in Fig. 1. It was concluded that the generation of the cracks in Fig. 1 was related to the forming temperature. In Fig. 16, there is one straight crack along the meridional plane, which is called the meridian plane crack, at the center of the conical crack. The maximum principal stress distribution of the central part of the glass is shown in Fig. 15 and can explain the meridian plane crack. Since the unit cycle time was changed, the strain rate and annealing/cooling rate were also changed. The problem of when the ring crack at the lens corner took place is not discussed in this paper. But this experiment indicates that the forming temperature was one of the factors that affected the generation of the cracks shown in Fig. 1.
Table 6. Processing Parameters in the Verification Experiments
Later, experiment No. 2 was performed, where the unit cycle time was set as 100 s and the other processing parameters were as shown for experiment No. 2 in Table 6. The forming pressure in the first forming stage was set smaller than that in experiment No. 1, while the forming pressure in the second forming stage was greater than that in experiment No. 1 to make the glass preform have enough deformation. Most of the lenses manufactured were crack-free. Some of the lenses are shown in Fig. 17. What should be pointed out is that when the air cylinder pressure was 0.6 MPa, the forming pressure was 10.07 MPa according to Eq. (5) when the diameter of the mold was 21 mm for the machine used in this paper. After the surfaces of the molds were compensated, the form errors of the molded lenses were stable.
5. CONCLUSION
One of the common types of fractures of molded lenses was studied in this paper. Based on the theory of fracture, a 3D simulation model was established in the software MSC Marc to investigate the formation and propagation of the divergent cone cracks. The experiments showed that the unit cycle time, forming temperature, and forming pressure were the contributing factors of the divergent cone cracks shown in Fig. 1. Therefore, the research results provide direction for optimizing processing parameters in the PGM process when such divergent cone cracks are generated in the molded lens. The method of analyzing lens fracture with the FEM using the fracture basis is effective. The direction for optimizing processing parameters can be deduced from the stress distribution components and principal stress in different stages of the PGM process for other types of lens fracture. The FEM model of the PGM process should continue to be improved in the future. Dynamical friction in the tangential direction and adhesion in the normal direction between the glass and the mold should be included in the established model for more accurate simulation results.
Funding
Key Science and Technology Program of Jilin Province (20180201030GX); National Natural Science Foundation of China (61905024); Science and Technology Development Program of Jilin Province (20200404197YY).
Acknowledgment
The authors thank Prof. Xue and Dr. Xing for their academic guidance.
Disclosures
The authors declare no conflicts of interest.
Data Availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
REFERENCES
1. T. F. Zhou, J. W. Yan, N. Yoshihara, and T. Kuriyagawa, “Study on nonisothermal glass molding press for aspherical lens,” J. Adv. Mech. Des. Syst. Manuf. 4, 806–815 (2010). [CrossRef]
2. Y. Zhang, G. P. Yan, K. Y. You, and F. Z. Fang, “Study on α-Al2 O3 anti-adhesion coating for molds in precision glass molding,” Surf. Coat. Technol. 391, 125720 (2020). [CrossRef]
3. L. Zhang, W. Zhou, N. J. Naples, and A. Y. Yi, “Fabrication of an infrared Shack–Hartmann sensor by combining high-speed single-point diamond milling and precision compression molding processes,” Appl. Opt. 57, 3598–3605 (2018). [CrossRef]
4. T. Zhou, J. Yan, J. Masuda, and T. Kuriyagawa, “Investigation on the viscoelasticity of optical glass in ultraprecision lens molding process,” J. Mater. Process. Technol. 209, 4484–4489 (2009). [CrossRef]
5. Y. Y. Zhang, R. G. Liang, O. J. Spires, S. H. Yin, A. Yi, and T. D. Milster, “Precision glass molding of diffractive optical elements with high surface quality,” Opt. Lett. 45, 6438–6441 (2020). [CrossRef]
6. P. He, F. Wang, L. Li, K. Georgiadis, O. Dambon, F. Klocke, and A. Y. Yi, “Development of a low cost high precision fabrication process for glass hybrid aspherical diffractive lenses,” J. Opt. 13, 085703 (2011). [CrossRef]
7. G. P. Yan, Y. Zhang, K. Y. You, Z. X. Li, Y. K. Yuan, and F. Z. Fang, “Off-spindle-axis spiral grinding of aspheric microlens array mold inserts,” Opt. Express 27, 10873–10889 (2019). [CrossRef]
8. L. Zhang, N. J. Naples, W. Zhou, and A. Y. Yi, “Fabrication of infrared hexagonal microlens array by novel diamond turning method and precision glass molding,” J. Micromech. Microeng. 29, 065004 (2019). [CrossRef]
9. Y. Liu, Y. Xing, C. Yang, C. Li, and C. Xue, “Simulation of heat transfer in the progress of precision glass molding with a finite element method for chalcogenide glass,” Appl. Opt. 58, 7311–7318 (2019). [CrossRef]
10. K. Li and F. Gong, “Numerical simulation of glass molding process for large diameter aspherical glass lens,” IOP Conf. Ser. 490, 052018 (2019). [CrossRef]
11. T. F. Zhou, J. W. Yan, J. Masuda, and T. Kuriyagawa, “Ultraprecision mass fabrication of aspherical Fresnel lens by glass molding press,” Adv. Mater. Res. 325, 713–718 (2011). [CrossRef]
12. C. Y. Huang, C. C. Chen, H. Y. Chou, and C. P. Chou, “Fabrication of Fresnel lens by glass molding technique,” Opt. Rev. 20, 202–204 (2013). [CrossRef]
13. C. Y. Huang, J. R. Sze, K. C. Huang, C. H. Kuo, S. F. Tseng, and C. P. Chou, “The glass-molding process for planar-integrated micro-optical component,” Opt. Rev. 18, 96–98 (2011). [CrossRef]
14. P. He, L. Li, J. Yu, W. Huang, Y.-C. Yen, L. J. Lee, and A. Y. Yi, “Graphene-coated Si mold for precision glass optics molding,” Opt. Lett. 38, 2625–2628 (2013). [CrossRef]
15. T. Zhou, Q. Zhou, J. Xie, X. Liu, X. Wang, and H. Ruan, “Surface defect analysis on formed chalcogenide glass Ge22 Se58 As20 lenses after the molding process,” Appl. Opt. 56, 8394–8402 (2017). [CrossRef]
16. L. Su, Y. Chen, A. Y. Yi, F. Klocke, and G. Pongs, “Refractive index variation in compression molding of precision glass optical components,” Appl. Opt. 47, 1662–1667 (2008). [CrossRef]
17. J. J. Nelson, Precision Lens Molding of Glass: A Process Perspective (Springer, 2020).
18. Y. Li, H. Huang, R. Xie, H. Li, Y. Deng, X. Chen, J. Wang, Q. Xu, W. Yang, and Y. Guo, “A method for evaluating subsurface damage in optical glass,” Opt. Express 18, 17180–17186 (2010). [CrossRef]
19. HOYA Co., “Optical glass data” [in Chinese], http://www.hoya-opticalworld.com/chinese/datadownload/index.html, accessed on May 30, 2021.
20. A. Symmons and M. Schaub, Field Guide to Molded Optics (SPIE, 2016).
21. H. H. Yao, K. Y. Lv, J. R. Zhang, H. Wang, X. Z. Xie, X. Y. Zhu, J. N. Deng, and S. M. Zhuo, “Effect of elastic modulus on the accuracy of the finite element method in simulating precision glass molding,” Materials 12, 3788 (2019). [CrossRef]
22. J. W. Pepi, Strength Properties of Glass and Ceramics (SPIE, 2014).
23. H. Wang, H. Chen, L. Xiao, B. Zhang, and Z. Jiang, “Fast predicting statistical subsurface damage parameters of the K9 sample,” Int. J. Optomechatronics 9, 248–259 (2015). [CrossRef]
24. J. H. Campbell, “Damage resistant optical glasses for high power lasers: a continuing glass science and technology challenge,” Glass Sci. Technol. 75, 91–108 (2002).
25. Y. Ahn, N. G. Cho, S. Lee, and D. Lee, “Lateral crack in abrasive wear of brittle materials,” JSME Int. J. Ser. A 46, 140–144 (2003). [CrossRef]
26. J. A. Wang, Y. G. Li, J. H. Han, Q. A. Xu, and Y. B. Guo, “Evaluating subsurface damage in optical glasses,” J. Eur. Opt. Soc. Rapid Publ. 6, 11001 (2011). [CrossRef]
27. A. K. Varshneya and J. C. Mauro, Fundamentals of Inorganic Glasses, 3rd ed. (Elsevier, 2019).
28. J. Ketkaew, W. Chen, H. Wang, A. Datye, M. Fan, G. Pereira, U. D. Schwarz, Z. Liu, R. Yamada, W. Dmowski, M. D. Shattuck, C. S. O’Hern, T. Egami, E. Bouchbinder, and J. Schroers, “Mechanical glass transition revealed by the fracture toughness of metallic glasses,” Nat. Commun. 9, 3271 (2018). [CrossRef]
29. R. C. Bradt, “The fractography and crack patterns of broken glass,” J. Fail. Anal. Preven. 11, 79–96 (2011). [CrossRef]
30. A. D. Salman and D. A. Gorham, “The fracture of glass spheres,” Powder. Technol. 107, 179–185 (2000). [CrossRef]
