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Abstract
During diving, high orbit maneuver, or target detection and positioning, a hypersonic vehicle will experience high thermal flux. Aerodynamic heating will cause intense thermal shock to the antenna window and radar dome, which are usually made of brittle materials that are transparent to electromagnetic waves and are critical to the mission of target positioning and hitting. Therefore, determination of the time to fracture of the brittle materials under high thermal flux is of great significance. In this study, thermal shock tests were performed on two brittle materials, i.e., SiO2 and Al2O3, using a quartz lamp radiator test system with a maximum thermal flux of 1.5MW/m2. The difference between the pre-set and actual thermal fluxes for the tests was smaller than 1.0%. The time to fracture was determined for the two brittle materials by employing the digital image correlation method to capture and analyze changes in speckle images of the specimen’s surface. The speckle image analysis also revealed variations in the surface strain values (εx and εy) prior to fracture. The test results provide important input for the safety and reliability design of radar domes and other electromagnetic wave-transparent signal detection and positioning components of hypersonic vehicles when subjected to high thermal fluxes.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The intense friction between the air and the surface of a flying hypersonic vehicle causes intense aerodynamic heating [1,2], especially during rapid diving, high orbit maneuver, and target positioning. Aerodynamic heating results in intense thermal shock to the antenna window, radar dome, and information detection devices, which are usually made of brittle materials that are transparent to electromagnetic waves and infrared waves such as microcrystalline glasses and high-temperature ceramics. Since components such as radar domes made of brittle materials are critical to a hypersonic vehicle’s capacity for target positioning and hitting, it is of great significance to monitor their stress and strain variation, fracture behavior, and time to fracture under high thermal flux.
There are reports on the thermal shock behavior of brittle materials in the literature. For example, Liang et al. [3] obtained the maximum thermal stress for a missile radar dome under thermal shock using numerical computation, and established a quantitative criterion for material fracture by performing a comparative analysis of the maximum thermal stress and the ultimate material strength. They also validated their computational results by performing arc-heated wind tunnel tests of radar domes under thermal shock. Wang et al. [4] suggested that tensile stress in ceramic materials will induce cracking, and proposed a critical temperature-characterized fracture criterion by performing thermal shock tests of ceramic materials. Qu et al. [5] obtained the critical temperature difference at the failure point of zinc sulfide (ZnS); a brittle material, by conducting thermal shock tests. They then compared the experimental results with numerical simulation results. Pettersson et al. [6] investigated the thermal shock resistance behavior of ceramic materials by testing β-sialons using the indentation-quench method. Chen et al. [7] tested the residual bending strength of brittle high-temperature ceramics subjected to rapid water cooling and analyzed the effect of the surface heat transfer coefficient on the thermal shock failure of the ceramics. He et al. [8] performed an experimental study of the thermal shock-resistance performance of ultra-high-temperature ZrB2-SiC ceramics using a self-made in situ test apparatus and computed the thermal stress distribution in the ceramics using numerical simulations. Panda et al. [9] studied the thermal fatigue behavior of alumina ceramics under the thermal shock of rapid cycles of alternate cooling and heating. They also investigated the effects of the initial crack length and temperature on the fatigue life of the ceramics.
There are mainly two methods for simulating the aerodynamic heating of hypersonic vehicles; high-temperature wind tunnel [10,11] and quartz infrared radiator [12–14]. For an aerodynamic heating simulation test using a convective-type high-temperature wind tunnel, it is difficult to capture the surface deformation and fracture information of the test specimen since it is enveloped by high-temperature thermal flows and intensive lights. Quartz infrared radiator heating is mostly used for rapid thermal shock tests under non-convective flows. The maximum heat flux created by the quartz lamp radiator heating system for a thermal shock test determines the maximum Mach number that can be simulated. The maximum thermal flux achieved by the NASA (US) using quartz lamp radiator heating is 1.13 MW/m2 [15], and that achieved by the thermal strength experimental center of the Russian ЦАГИ is 1.0 MW/m2 [16]. The design speed of hypersonic vehicles keeps increasing. Therefore, for continual application for thermal shock simulation tests, quartz lamp radiator heating systems must be capable of simulating greater thermal fluxes.
The process for a hypersonic vehicle to position a target usually takes a very short time, typically in the range of a few seconds. The viability of a radar dome after a thermal shock test cannot be determined until after it is cooled, and the cooling process takes a relatively long time. Suppose that the effective time for a hypersonic vehicle to position a target is 4 s and its radar dome experiences cracking or fracture after a thermal shock test, it is not known whether the tested radar dome is damaged during the 4 s or the subsequent cooling process. If the damage occurs during the 4 s, then the radar dome is unacceptable; if the damage occurs after the 4 s, the radar dome is acceptable, since the damage is subsequent to the positioning of the target. Therefore, determination of the exact time to fracture of the radar dome material is extremely desirable for hypersonic vehicle designers, since this parameter constitutes an important criterion for them in the selection of appropriate materials, the optimization of geometry and structure, and the determination of structural thickness and other critical parameters of the radar dome. Previous thermal shock studies of brittle materials mainly focus on the fracture mechanism and failure criterion. However, there are few reports on the time to fracture and surface strain variation of brittle components under high thermal flux.
In this study, two brittle materials; SiO2 and Al2O3, were tested under large rapid high thermal flux, using a self-made thermal shock test system. The rapid thermal shock test system uses a quartz lamp infrared radiator heating (applied laterally from a single side in an aerobic environment) to simulate aerodynamic heating and the maximum thermal flux was 1.5 MW/m2. The time to fracture was successfully determined for the specimens by utilizing the digital image correlation method to image changes in the deformation of the brittle materials (sprayed with a thin layer of speckles). The speckle images were analyzed prior to the fracture and computed to obtain the variations in the surface strain values (εx and εy). The experimental results will provide important inputs for safety and reliability design of radar domes and other electromagnetic wave-transparent signal detection and positioning components of hypersonic vehicles under high thermal flux.
2. Test specimens
Figure 1(a) shows the SiO2 specimen with a smooth surface that measures 100 x 100 x 5.1 mm. Since SiO2 is transparent to lights, the specimen was pretreated to induce surface blackening and sprayed randomly with speckles, such that a CCD camera could be used to record the instantaneous changes of the specimen’s surface. This allowed the digital image correlation method to be utilized to image changes in the surface displacement field. Figure 1(b) shows the Al2O3 ceramic specimen that measures 100 x 100 x1.8 mm. The specimen was also blackened and sprayed with white speckles.
The white speckles were made using a custom-made high-temperature white inorganic glue with the main ingredients of silicate and alumina. The speckles have an adhesion strength of 8 MPa and a linear expansion coefficient of 8 × 10−6/°C (very close to that of SiO2 and Al2O3 materials). Therefore, the speckles have a good adhesion and stability at high temperatures. The white solid speckles (powder) were blended with a transparent curing agent. The blend was evenly mixed then subsequently sprayed onto the specimens as markers. The inorganic glue consists of two components, the ratio of which can be fine-tuned to adjust the viscosity. The thickness of the speckle layer was controlled to less than 0.15 mm. The layer of the randomly sprayed speckles (used as markers for the tests) had a minimum thickness and weight compared with those of the specimens. Moreover, their expansion coefficient was close to that of the specimens, so their effect on the deformation of the specimens was insignificant [17].
3. Experimental setup
Figure 2 shows a schematic illustration of the infrared radiator thermal shock experimental setup with an array of quartz lamps as the heat source. A sandwich-type water cooler was mounted behind the quartz lamp array. The cooler surface was polished to reflect the radiation from the infrared arrays from the quartz lamp array in order to improve the heating efficiency. The specimen was vertically mounted at the center of the other side of the sandwich-type water cooler. To minimize heat loss, the specimen was surrounded by an insulation frame made of a lightweight porous ceramic material with a very small thermal conduction coefficient. The water cooler measured 500 x 500 mm from the side view whereas the quartz lamp array measured 400 x 400 mm from the side view. The distance between the front row of the quartz array and the front surface of the specimen was 50 - 70 mm. The water cooler operates by circulating cooling water.
Fig. 2 Schematic illustration of the quartz lamp infrared radiator heating high thermal shock experimental setup.
In order to increase the radiative heating capacity of the quartz array, the two rows of quartz lamps were arranged in an alternating manner such that the heat radiated from the back row passed through the gaps between the lamps of the front row. This arrangement of the quartz lamp array not only greatly improved the density of the thermal flux radiated onto the specimen surface, but also contributed to a more even temperature field on the specimen’s surface. The thermal flow sensor was mounted below the specimen, with the sensor’s detection plane aligned with the specimen’s surface. This configuration was implemented because it can prevent the influence of fog-type thermal flow diffusion on the thermal flow sensor. A large array of quartz lamps was designed to ensure that the specimen and the thermal flow sensor experience the same thermal environment during thermal shock testing. In order to improve their reliability, the quartz lamps were surface-cooled by air flow circulation. As a result of these measures, it was possible to generate a maximum thermal flux of 1.5 MW/m2 using the experimental setup. The test system was also capable of controlled nonlinear thermal environment simulation with a temperature increase rate of 210 °C /s [18], thermal-vibration test at high temperatures up to 1200 °C [19], and thermodynamic test in high-temperature (1500 °C) oxidization environments [20]. Figure 3 is an image of the thermal shock experimental setup.
4. High thermal shock test
Figure 4 shows the thermal flux setting curve for the thermal shock tests. The results indicate that the thermal flux was set to reach a maximum value of 1.5 MW/m2 within 4 s. The tungsten filament of the quartz lamp has a very small electrical resistance at the room temperature which is usually a fraction of the value at high temperatures. The filament of the quartz lamp breaks if it experiences a very large instantaneous impulse current at the initial stage of the heating process. Generally, the filament of the quartz lamp needs to be preheated for a short period of time prior to the test. Therefore, the thermal flux setting curve begins with a 0.5-s stage of preheating (the beginning section of the curve with a small slope) in order to ensure the reliability of the quartz lamps. The high thermal shock stage begins after the 0.5-s preheating stage. Figure 4 also shows the actual controlled thermal flux curve. The figure shows that the thermal flux setting curve basically overlaps or is consistent with the actual controlled thermal flux curve. Table 1 provides a summary of the actual thermal flux values measured during thermal shock testing versus the corresponding settings. The data demonstrate that the difference between the actual measurements and the setting values was smaller than 1%. This confirms that the thermal shock test system was capable of accurate simulation of dynamic high thermal shock conditions.
Table 1. Preset and Actual Thermal Flux Values for the Thermal Shock Test
5. Time to fracture
Figure 5(a) present images of the SiO2 specimen prior to and after thermal shock-induced fracture captured by a CCD camera. Figure 5(a1) shows the specimen after 2.998 s of testing when the specimen exhibited no cracking. After 3.048 s of testing (Fig. 5(a2)), the specimen exhibited noticeable network-like cracks. Figure 5(a3) shows the specimen after fracture and additional cracks are evident. Figure 5(b) represents images of the Al2O3 specimen prior to and after thermal shock-induced fracture. After 2.640 s of testing (5(b2)), the specimen exhibited an oblique crack running through its surface. The crack continued to expand with the progression of testing. Using the time-series of the speckle images obtained from thermal shock testing, the time to fracture of brittle materials; a critical parameter for determining whether or not they meet specific safety design requirements, can be determined.
Fig. 5 Photographs of specimen before and after the fracture point under thermal shock. (a) SiO2. (b) Al2O3.
6. Measurement of surface deformation fields
The digital image correlation method is a technique for measuring image information by performing numerical calculation to compare changes in images of an object before and after surface deformation. By tracking the changes in the position of a speckle point in the images before and after deformation, information about the surface displacement of the measured object can be obtained [21–23]. Therefore, based on the digital image correlation method, the changes of surface strain εx and εy prior to fracture of brittle specimen under thermal shock can be acquired.
The basic principles of the digital image correlation method are shown in Fig. 6. First, a square subarea with a center at P(xi,yi) is selected from the reference image (reference subset). After the deformation, a searching subset is defined in the deformed image, and several square deformed subsets with the same size as the reference subset are successively selected from the searching subset at a certain step length. The position of the target subset’s center point, P’(x’i,y’i), can be obtained by performing correlation calculations between the reference subset and the deformed subsets in the searching subset in accordance with a predetermined correlation function.
The expressions for the correlation function used to evaluate the degree of similarity between the speckle images before and after the deformation are
Where f(x,y) represents the gray scale of the coordinate point (x,y) in the image reference subset, g(x’,y’) represents the gray scale of the coordinate point (x’,y’) in the image target subset, and P is the displacement vector. The extrema of the correlation function C for the speckle images before and after the deformation were determined
The displacement of the reference subset’s center point can be obtained through an iterative algorithm that determines the relevant parameters of the displacement vector P. The in-plane strain of the speckle images can be obtained by deriving the displacement function in a corresponding direction
A rectangular calculation area of 1288 × 1078 pixels was selected from the speckle images of square SiO2 specimen. During the analysis and calculation, the size of the subarea in the reference image was 43 × 43 pixels, and the distance between adjacent calculation points was 7 pixels; there was a total of 28675 calculation points.
Figure 7(a) represents three isograms for in-plane displacements of the SiO2 specimen prior to fracture, which were obtained using the digital image correlation method for the three time points of the test i.e., 1.994, 2.396, and 2.896 s. The isograms demonstrate that as the specimen approaches fracture, its surface displacement isolines exhibit greater fluctuation and discreteness, and more ring-like isolines are formed. This implies an increasingly uneven specimen surface deformation and local stress concentration, which finally results in fracture failure of the specimen. Figure 7(b) represents three isograms of the in-plane displacements of the Al2O3 specimen at three time points of the test i.e., 0.742, 1.820, and 2.590 s. The isograms demonstrate that the surface deformation and in-plane strain variation of the Al2O3 specimen increase with an increase in the thermal flux.
Figure 8(a) represents the time series of the surface strains of the SiO2 specimen computed using the speckle images. The figure shows that the strains (εx and εy) first increase then subsequently decrease with the progression of testing. In reference to the thermal flux curve (shown in the right upper corner of Fig. 8(a)), in the first 0.5 s of testing, the thermal flux increased marginally (from 0 to 42 kW/m2), and the specimen expanded under the influence of heating. This explains the increase in the strain at the beginning stage of the test. When the test entered the rapid thermal shock stage after 0.5 s of preheating, the specimen surface temperature increased rapidly under the influence of the rapid thermal shock (thermal flux increased by 375 kW/m2 per second). Due to the time difference in thermal conduction between the back and front surfaces of the SiO2 specimen (5.1 mm in thickness), the temperature increase of the back surface of the specimen lagged that of the front surface. Thus, there existed a very great temperature difference between the back and front surfaces. Therefore, there was a significant difference in the thermal expansion-induced deformation. Consequently, the specimen bent towards the back surface (with a lower temperature), where compress strains (designated as negative values) were experienced. After the 0.5 s of preheating, the absolute value of the strain increased with the rapid increase of the thermal flux on the front surface and peaked at the time of fracture. The curve of the strain in the x-direction (εx) exhibited a turning point towards the end of the test, as shown in Fig. 8(a). This is because when a turning point occurs in the x-direction of the specimen, the stress in the direction relaxed.
Figure 8(b) represents the time series of the strain values for the back surface of the Al2O3 specimen computed from the speckle images. Since the thickness of the Al2O3 specimen (1.8 mm) was much smaller than that of the SiO2 specimen (5.1 mm), the thermal hysteresis-induced bending deformation of the first specimen was much smaller than that of the second specimen. The time series of the surface strain (Fig. 8(b)) exhibited a continuously increasing trend because of the combined effect of the thermal shock-induced thermal expansion and bending deformation.
Figures 9(a) and 9(b) show the micro-morphological structures of the fracture surfaces of the SiO2 and Al2O3 specimens, respectively. The fracture surface of the Al2O3 specimen (Fig. 9(b)) exhibits densely and evenly distributed micro indentions, while that of the SiO2 specimen (Fig. 9(a)) exhibits irregularly distributed microcracks. The development of these irregular cracks affected the continuity and smoothness of the surface strain variations and eventually led to the fracture of the SiO2 specimen (Fig. 9(a)).
Fig. 9 Micrograph of the fracture surface of the specimen (magnification 4000). (a) SiO2. (b) Al2O3.
7. Conclusions
- 1) A water-cooling infrared-radiation rapid thermal shock test system was developed with a maximum thermal flux of 1.5 MW/m2. The difference between the preset thermal fluxes and the actual thermal fluxes for the thermal shock test was smaller than 1.0%. The consistency between the preset and actual thermal flux demonstrates the test system’s capability to simulate accurate rapid thermal shock.
- 2) The digital image correlation method was employed to obtain speckle images and to compute surface strain values (εx and εy) for the test specimens of two brittle specimens prior to thermal shock fracture.
- 3) As the specimens approached fracture, they exhibited greater and more uneven surface deformation in addition to a greater degree of local stress concentration, as revealed by the more discrete isolines for in-plane surface displacement.
- 4) The time to fracture; a critical design parameter for brittle materials, was determined using surface morphological images captured by a CCD camera. The time to fracture obtained for the test specimens can then be used to determine whether or not brittle materials can meet structural safety design specifications. This type of analysis is particularly important for hypersonic vehicles. The experimental results are of great significance with regard to safety and reliability design of hypersonic vehicles, as well as their capability for target positioning and hitting.
Funding
National Natural Science Foundation of China (11427802).
Acknowledgments
The authors gratefully thank National Natural Science Foundation of China for providing scholarship to support the research reported in the paper.
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