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Abstract
High-temperature deformation measurements based on optical measurement techniques are important for studying material properties. Due to the existence of temperature gradients between the high-temperature subject and the imaging system, the uneven air density distribution leads to random changes in the refractive index of air along the beam transmission path, which triggers random jitter in the images captured by the imaging system, resulting in large errors in the measured displacement field. In this paper, a dual speckle method is developed for eliminating air distortion in high-temperature experiments. The main experimental setup consists of two cameras, where one camera is focused on the speckles sprayed on the specimen surface that can measure the coupled displacement field, and the other camera is focused on the semipermeable speckles, which can measure the pure displacement caused by the change in the refraction index of air. Then, the true displacement of the tested specimen can be obtained by an arithmetic operation after the calculating point meets the one-to-one relationship. A simplified yet effective test was conducted and verified the feasibility of the method proposed, as the error analysis was analyzed in detail.
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1. Introduction
High-temperature deformation measurement techniques have been widely used in the characterization of high-temperature mechanical properties of materials [1]. Deformation measurement in extremely high temperatures is always a hot topic in experimental mechanics, especially in photo mechanics with advantages of non-contact, full-field and real-time measurement. A variety of optical methods have been proposed for surface deformation measurements at elevated temperatures, for instance, interferometric strain/displacement gage, moiré interferometry, electronic speckle interferometry and laser speckle correlation technique, of which are all interferometric techniques [2,3] with the disadvantages of the coherent light source and vibration-isolated optical platforms, and non-interferometric techniques, like video extensometer and digital image correlation (DIC) [4–6].
In the past decades, the DIC method, which is a useful tool for measuring displacement and stress distributions during mechanical testing, has made enormous progress since it was developed [7]. At low temperatures, the DIC method is good in use. However, when it comes to high temperatures (approximately 1000 °C) for acquiring sample surface with sufficient contrast, serious issues will occur that have to be considered in order to measure displacement and stress accurately and robustly, like black-body radiation, oxidation, and heat haze [8] with another saying “air distortion”. The first issue has been solved well in the literature [8] by suppressing black-body radiation through the use of filters together with blue illumination, in which the remaining two factors were that a vacuum chamber would be feasible to measure strain, avoiding significant changes of surface features in heating progress and also eliminating any possible heat haze effects. The imperfectness of the optical window and the variations in the refractive index of the heated air were also analyzed for their strong influence on the measured fields, and a van was added near the furnace window to blow air perpendicular to the camera’s focal axis, avoiding the transient variations in the refractive index of air. At present, the air distortion suppression is mainly done by hardware improvement or experimental device improvement to reduce the impact of air distortion on beam transmission. Strycker [9] pointed out through analysis that the problem of air distortion due to temperature gradients that occur around high-temperature subjects can be mitigated by arranging an air knife for air distortion stabilization. Novak et al. [10] considered that the problems of the thermomechanical response of materials at high temperatures involve illumination, heat haze, surface contrast, and the apparent distortions caused by heat haze were reduced by an air knife, whose role is to minimize thermal turbulence and thoroughly mix the air. Wang [11] used the DIC method to measure the thermal deformation of thin film samples at 160 °C. Because of the optical glass window installed in the heating chamber and the airflow field formed on the outside of the glass window due to uneven air temperature distribution, the authors proposed installing a pneumatic device on the side and using an air knife to cool the air in the beam transmission path. In 2018, Jones and Reu [12] analyzed the effect of a non-uniform refractive medium caused by airflow perturbation on the measurement accuracy of the DIC displacement field and used an air knife to stabilize the non-uniform refractive medium. In 2019, Reu [13] proposed performing high-temperature heating experiments in a vacuum test chamber to achieve the effect of suppressing air distortion. The aforementioned method has limitations in terms of applicability due to the large modification of the test apparatus and does not applicable to the case of heating in an open environment. A simple yet effective speckle pattern fabrication technique was proposed by Pan [14], in which a commercial high-temperature inorganic adhesive was used to blend black cobalt oxide with the liquid composition, and the experimental results show that the speckle pattern can sustain a high temperature exceeding 1100 °C compared with the common decorative paints being burned out when the environmental temperature exceeds 250 °C. But the influence of the change in the air refraction index was ignored, as the deformed images were recorded after the desired temperatures were stable, as in the author’s other work [4]. Liu et al. [15,16] proposed a simple high-temperature resistant speckle manufacturing technology where artificial speckle patterns with random variations of gray scale intensity were made on the thermal barrier coating interface, with high oxidation resistance and sufficient contrast to warrant reliable correlation analysis. A hot air baffle plate was designed to exclude the effects of fire on the images, or in other words, to eliminate the phenomenon of image distortion caused by changes in the refractive index of the air. Aswendt P [17] has also done a systematic study of disturbing influences and their suppression in the early 21st century. In the experiment, speckle interferometry was used, in which the thermal emission could be excluded by an interference filter and a high-power laser, and the current in the air could be eliminated by a vacuum or laminar flow.
As the literature mentioned above, the influence of air distortion was all taken care of. However, it was not completely eliminated by all the methods put forward. A vacuum, which is too costly, can exclude the influence of the change of the refraction index of air, but the vacuum environment is not exactly the service environment of most materials in the presence of oxygen. To some extent, laminar flow or a van can reduce the effect of air distortion, but for accurate measurement, the change in the refraction index of air will introduce errors in the final result, which cannot be ignored. Figure 1 shows the effect of air distortion.
Fig. 1. The speckle image (a) without and (b) with air distortion and the calculated displacement field in the (c) x direction and (d) y direction, respectively.
In this paper, a dual speckle method is developed for eliminating air distortion in high-temperature experiments. The test system consists of two cameras, where one camera is focused on the speckles sprayed on the specimen surface that can measure the coupled displacement field, and the other camera is focused on the semipermeable speckles, which can measure the pure displacement caused by the change in the refraction index of air. Then, the true displacement of the tested specimen can be obtained by an arithmetic operation. The theory of the proposed method in combination with the real situation of the samples tested at elevated temperatures is interpreted in detail. A simplified validation test is performed completely and the error factors possibly affecting the measurement result are discussed comprehensively.
2. Theory
Here, a novel optical measurement method that can be applied to elevated temperature measurements is proposed, in which a highly translucent glass (the observation window) with semipermeable speckle placed in front of the specimen can measure the air distortion, and the high-temperature resistant speckle sprayed on the specimen can measure the coupled deformation field composed of specimen deformation and air distortion. The schematic diagram is shown in Fig. 2. The dual speckle test system consists of a loading system, a high-temperature furnace with an observation window, a semi-transparent mirror, a mirror parallel to the semipermeable membrane, and two CCD cameras. The semi-transparent mirror was placed in front of the furnace. The CCD1 and CCD2 focus on the high-temperature resistant speckle and the semipermeable speckle through the green light path and red light path, respectively.
In order to study the mechanical properties of materials in a coupled thermal-mechanical environment, a high-temperature furnace is always used to simulate the real condition. As shown in Fig. 2, a heating furnace compared with a stretching/compression device can study the thermodynamic properties of materials. The coupled deformation field composed of the real deformation field and the deformation field caused by air distortion can be obtained by the high-temperature resistant speckle sprayed on the sample using the high-temperature digital image correlation (DIC) method introduced in detail in the literature [4], and the semipermeable speckle fabricated on the observation window of the furnace can only measure the deformation field of air distortion. To ensure that the two cameras can focus on the same region via the same path, a semi-transparent mirror combined with a reflecting mirror was used. Then, using the two deformation fields, the real deformation condition of the specimen can be obtained
where, ${U_r}$, ${U_c}$, and ${U_a}$ represent the real displacement of the specimen, the coupled displacement field and the displacement field caused by the change in the refraction index of air, respectively.To realize the proposed method, two major influence factors must be taken care of:
- (1) The one-to-one correspondence of the two sets of speckles spatially;
- (2) The interaction between the two sets of speckles.
As the two sets of speckles are captured by two sets of acquisition systems, the initial mismatch of the two systems should be excluded. The specimen was placed parallel to the observation window spatially in the preparation stage. In order to get the one-to-one relationship between the two sets of speckles, the two cameras should first be adjusted to focus on one of the speckles: the semipermeable speckle or the high-temperature resistant speckle. By doing this, the mismatch of the speckles will occur, as shown in Fig. 3. The figures AB and A’B’ represent the speckle pattern captured by the two cameras. The rigid body movement and the relative angle can be directly obtained and eliminated by the two images taken by the two cameras focusing on the same speckle using a correlation algorithm. In fact, when the displacement field is calculated using the DIC method, an important procedure is to choose a region of interest (ROI). If there is a one-to-one correspondence between points A and A’ and so are points B and B’, the whole ROI of the two images captured by the two cameras will be in a one-to-one relationship. Then, one of the two cameras will be adjusted to focus on the other speckle pattern. As is shown in Fig. 2, CCD1 is focusing on the high-temperature resistant speckle pattern and CCD2 is focusing on the semipermeable speckle pattern, and the only difference between the images taken by the two acquisition systems is magnification that can be calibrated (see Fig. 3(c)).
Fig. 3. Schematic diagram of the initial relative error of the two acquisition systems: (a) rigid body movement, (b) relative angle, and (c) magnification difference.
Actually, the semipermeable speckle is placed in front of the high-temperature resistant speckle, so the two speckle patterns will influence each other. In order to eliminate the interaction of the two speckle patterns, various attempts were made. It is found that when the distance of OO’ (see Fig. 5) is suitable for a certain condition, the influence between the two speckles can be ignored. Each lens has a certain focal length and depth of field, meaning that the images captured will be displayed clearly if the object is within the scale of the depth of field, but fuzzy if the object is outside of the scale of the depth of field. The fuzzification of the images was used to separate the interaction of the two speckles. When the camera focuses on one of the speckles, the other speckle will be dimmed, just like improving the gray scale overall like in Fig. 4. Some stubborn black spots are like dust on the CCD chip. Thanks to the development of the DIC technique [16,18,19], the dust will not affect the calculation results, meaning that the problem can be well solved.
Fig. 4. (a) Specimen speckle pattern, semipermeable speckle placed in front of the specimen speckle pattern (b) before and (c) after adjusting the aperture, and (d) semipermeable speckle pattern.
3. Experiment and discussion
A simplified validation test was conducted to verify the correctness of the developed method. As shown in Fig. 5, the specimen used was silicone rubber with a pre-crack marked with a red circle to lead to stress concentration when the sample was stretched. The experimental setup consists of a tensile testing machine, a silicone rubber, a quartz glass, a ring illuminator, an alcohol lamp used to heat air, a semi-transparent mirror, a reflecting mirror and two acquisition systems composed of a DH-HV 1310 FM CCD installed with an AVENIR CCTV lens (SR12575).
The experiments were carried out as follows:
- (1) The experimental system was set up according to the optical path, as shown in Fig. 5. The silicone rubber with a pre-crack was sprayed with paint to form an artificial speckle. The semipermeable speckle sprayed on the quartz glass was composed of a mixture of ink and water with a volume ratio of 1:3 to 1:4.
- (2) The two sets of speckles were revised to one-to-one correspondence mentioned in part 2. The image acquisition software was started and the focal lengths of the lens were all adjusted to focus on the specimen speckle on the silicone rubber. After calculation, the rigid body movement, relative angle and magnification difference were obtained and revised. Then the CCD2 was adjusted to focus on the semipermeable speckle and the magnification difference between the two cameras was also calibrated and revised.
- (3) Image acquisition was triggered. Images of the two sets of speckles taken as reference images were captured and stored by both image acquisition devices.
- (4) The testing machine was started with an automatic control displacement controlling loading step, with a step size of 0.5 mm and a time interval of 15 s between two steps. The images of the high-temperature resistant speckle containing the coupled deformation information and the semipermeable speckle including the air distortion information were all captured and stored as soon as the current step ended. Then the alcohol lamp would be fired as quickly as possible and the images taken simultaneously to avoid the possible creep of the silicone rubber during the two collections.
- (5) Image analysis was carried out using the DIC procedures, using the deformation of the specimen during the tensile test compared with the factor of air distortion.
The two acquisition systems were first focused on the specimen speckle, and then the initial mismatch between the two systems could be calculated, as shown in Fig. 6. The differences between the two systems are rigid body movement and magnification difference, and there is hardly any relative angle between the two CCDs that can be obtained from the displacement vectors of Fig. 6(d).
Fig. 6. The displacement field of the initial difference between the two acquisition systems showing (a) u-field displacement, (b) v-field displacement, (c) the correlation map, and (d) resultant displacement with displacement vectors.
After the mismatch was calibrated and revised, meeting the one-to-one relationship, the CCD2 was adjusted to focus on the semipermeable speckle. The difference in magnification between the two systems was calibrated and revised for further calculation.
The test was conducted as per the procedures specified above with a displacement load of 3 mm, and the result is illustrated in Fig. 7. The ROI was set next to the pre-crack as the red rectangle marked in Fig. 5. The result only shows the u-field displacement since the u-field displacement has a distinct stress concentration phenomenon that would make it easy to compare the results. There is an obvious big difference, no matter the peak value or the shape of the displacement field, between the coupled displacement field and the pure tension field, as shown in Fig. 7(a) and (d), indicating that the air distortion indeed has a significant influence which cannot be ignored on the final result. As shown in Fig. 7(e), the influence of changes in the air refraction index was well eliminated in most areas, but the relative error is relatively large in the region of the crack tip marked in a red dashed circle. Actually, the two acquisition systems controlled by two computers of the same type were triggered at the same time, taking the display lamps mounted in the back of the camera off-line simultaneously as the signal. However, the time difference caused by the hardware and software of the two systems in transmitting signals may be large enough that it cannot be neglected or ignored in this paper. In other words, the air distortion recorded in the images of the coupled field and the pure distortion field was not completely equivalent, causing the relative error in the local region to become larger. Ma [20] has systematically analyzed the systematic error in photomechanical methods induced by camera self-heating. The influence of camera self-heating may be another factor that led to the relative error being a little larger than expected.
Fig. 7. The deformation of the silicone rubber showing (a) u-field displacement of the coupled field, (b) u-field displacement of pure air distortion, (c) u-field displacement of calculated value, (d) u-field displacement of pure tension value, and (e) relative error.
Additionally, researchers have also done some work on algorithms for air distortion suppression. SU [21] proposed an effective gray-scale averaging technique to minimize the effect of thermal fluctuations on the accuracy of strain measurements in high-temperature environments. However, the image gray-scale averaging method is only applicable to quasi-static heating processes such as in thermal expansion experiments and does not work for deformation measurements at high-temperature vibrations. Li [22] proposed a two-dimensional UV digital image correlation system to obtain high-quality speckle patterns by minimizing radiation effects and using an air controller combined with an image averaging algorithm to reduce the effects of different thermal fluctuations for testing temperatures up to 1200 °C. Here, the effect of the algorithm on the measurement results is not discussed in depth.
4. Conclusion
Due to the difficulties of eliminating the change in the refraction index of air in the high-temperature DIC method, a novel dual speckle method was developed and a two-CCD capture system was established. In the acquisition systems, a camera was focused on the specimen speckle and the other was focused on the semipermeable speckle. The coupled displacement field and the pure air distortion field can be distinguished. After the calculated point was set into a one-to-one relationship, the influence caused by the change of the refraction index of air could be completely excluded. A simplified yet effective test was conducted, and the relative error can be controlled to less than 5% on average.
Further studies of eliminating the error factors systematically and accurately with the aid of this method will be conducted in future work.
Funding
Fundamental Research Funds for the Central Universities (No. BLX201915); National Natural Science Foundation of China (12002053, 11972084); Beijing Municipal Natural Science Foundation (1204033,1192014); National Science and Technology Major Project (2017-V1-0003-0073).
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.
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