Figures 1-4
Figures 5-7

Knowledge of the mechanical behavior of materials at elevated temperatures is vital for the design of structural components in various fields such as aerospace, automotive, and nuclear engineering. It is desirable to visualize the response of the structure to applied loads under actual working conditions. Conventional invasive transducers such as strain gages, which provide local strain information, may not be reliable at extremely high temperatures. Optical noninvasive measurement techniques such as holography, speckle interferometry, and moiré are attractive for material testing at high temperatures because they provide full field displacement and strain information.

Earlier optical work related to full field displacement and strain measurements on very hot objects is rather scarce. According to a review article (Sciammarella, 1982), moiré techniques have been used to measure in-plane deformations up to 600 ºC (1,112 ºF). Measurements in the same temperature range, using the high resolution moiré technique, have also been reported (Burch and Forno, 1982). Speckle photography was applied for the measurement of strains up to 900 ºC (1,652 ºF) by Stetson (1981). Kang et al. (1990) reported the application of high sensitivity moiré interferometry for the measurement of deformations up to 550 ºC (1,022 ºF). In ordinary holographic interferometry, there is the early work of Evensen et al. (1972), who used a pulsed laser to record the vibrations of panels heated up to 1,150 ºC (2,102 ºF). Lockberg et al. (1985) and Malmo et al. (1988) employed electronic speckle pattern interferometry for the visualization of deformation fringes in objects above 1,000 ºC (1832 ºF). This paper presents an electronic speckle pattern interferometric technique which can be used for the quantitative measurement of displacement and strains at very high temperatures.

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Electronic speckle pattern interferometry is an attractive technique for the characterization of materials at elevated temperatures.

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Electronic Speckle Pattern Interferometry
Electronic speckle pattern interferometry (ESPI) is also called electro-optic holography or TV holography, in the literature. Extensive literature on the application of ESPI for the measurement of static and dynamic displacements at normal temperatures can be found in Holographic and Speckle Interferometry (Jones and Wykes, 1989). Figure 1 shows an ESPI system which can be used to measure in-plane displacements and strains. The test object is illuminated using two laser beams which make equal angles with the surface normal to the object. The image of the object is formed on the detector of a video camera using a system of lenses. The image captured by the video camera is processed using a digital image processor.

To obtain the fringes corresponding to the displacement field, two images of the object are needed: one before deformation, and the other after deformation. The image of the object illuminated by laser light has a random distribution of speckles, which are extremely sensitive to the motion of the object's surface. The intensity distribution in the image of the object before deformation can be expressed as

(1)

where I₀(x, y) is the background intensity, I₁(x, y) is the amplitude and ø (x, y) is the relative phase between the two interfering light waves (Jones and Wykes, 1989). Intensity distribution in the image of the object after deformation can be expressed as

(2)

where ø (x, y) is the phase change due to the deformation field. Subtractive superposition of the two images above produces a fringe pattern corresponding to the deformation field, which can be written as,

(3)

The term [1 - cosø (x, y)] in Equation 3 represents the fringe pattern corresponding to the deformation field; the remaining terms constitute the background noise. The deformation fringe can be observed in real time by performing the superposition of the two images inside a digital image processor.

Equation 3 was derived under the assumption that the deformation field introduces change in the phase of the speckles in the image of the object only, leaving their amplitudes unchanged. In practice, however, there is also a small change in the amplitude of the speckles due to object deformation. The amplitude of the speckles can also change due to oxidation of the object surface. In view of this, an equation governing the deformation fringe pattern can be expressed as:

(4)

where I_b(x, y) is the background intensity and (x, y) is the fringe visibility. The phase change ø (x, y) corresponding to the deformation field can be separated from the noisy background using the digital filtering technique (Sciammarella and Bhat, 1991). The displacement field can then be obtained by multiplying the phase map by the sensitivity constant for the optical system and the strain field can be computed by differentiating the displacement field.

 

Measurement of Deformations and Strains at High Temperatures
ESPI is applied for the measurement of in-plane deformations and strains at high temperatures. In the first experiment, the technique is used to measure the coefficient of thermal expansion of a rectangular bar of Haynes alloy No. 25. The specimen is heated in an oven which can attain a temperature of 1000 ºC (1832 ºF). The oven has three windows made of high temperature glass, two for laser illumination and the third for observation. The temperature inside the oven is measured using three thermocouples and the temperature is regulated using a temperature controller.

The specimen is heated to the desired temperature inside the oven. After the temperature is stabilized, the reference image is captured and stored in the image processor. The temperature is increased by 10 ºC (18 ºF) and the second image is captured after the temperature is stabilized. Fringes corresponding to the thermal expansion are obtained by the subtractive superposition of the two images above. Figure 2, for example, shows the thermal expansion fringes in the Haynes alloy bar at 1,000 ºC (1,832 ºF). A digital filtering technique is employed to analyze the fringes and obtain the elongation of the bar due to thermal expansion. Then, the coefficient of thermal expansion is obtained using the relation

(5)

where L is the initial length of the bar, L is the change in length due to thermal expansion, and T the temperature gradient applied to the specimen. Figure 3 shows a plot of the thermal expansion coefficients of Haynes alloy No. 25 measured at high temperatures, along with the values supplied by the manufacturer, which are based on the expansion of the specimen occurring between room temperature and the desired temperature, whereas the values obtained using speckle interferometry are local values at the desired temperature.

In the second experiment, ESPI is employed for the measurement of strains in a disk of Haynes alloy, subjected to diametral compression at 1,000 ºC (1,832 ºF). The optical setup is the same as that used for the first experiment. A loading device is incorporated within the oven used for heating the specimen. The specimen is supported on a rigid ceramic base and the diametral compression is applied using a pneumatic cylinder with a piston.

The specimen is held at the desired temperature inside the oven and subjected to diametral compression. The displacement fringes are obtained by superimposing the image of the object before loading with that after loading. A digital filtering technique is used to analyze the fringes and obtain the displacement and strain fields. Figure 4, for example, shows the fringes (noise-free) corresponding to the displacements perpendicular to the loading direction, in the central portion of the Haynes alloy disk, obtained at 1,000 ºC (1,832 ºF). Figures 5 and 6 show the displacement and strain fields corresponding to the fringe pattern above, respectively.

Since the deformation fringes are displayed on a video monitor in real time, it is possible to visualize the material creep at high temperatures. Figure 7, for example, shows the fringes due to creep in the Haynes alloy disk held under constant diametral load, at 1,000 ºC (1,832 ºF).

 

Problems Encountered at High Temperatures
Several problems are encountered while recording images at high temperatures. When the specimen is heated up to 1,000 ºC (1,832 ºF), its surface starts oxidizing. This oxidation changes the surface texture of the object, which results in the decorrelation of the speckles in the image of the object. Decorrelation of the speckles results in a drastic reduction in the visibility of the displacement fringes. This oxidation of the specimen surface can be prevented by coating it with a ceramic paint which can withstand high temperatures.

When the object is heated, it starts radiating energy at various wavelengths. The energy radiated by the object surface at 1,000 ºC (1,832 ºF) is much stronger than energy of the laser light scattered from its surface. The radiation is recorded by the video camera as a background bias, which results in reduction in the visibility of the speckles and, hence, that of the displacement fringes. If the radiation is sufficiently strong, it may even saturate the camera detector. The background radiation can be prevented from reaching the camera detector by introducing a narrow band interference filter in front of the camera, which passes wavelengths near the laser wavelength only.

Another problem encountered at high temperatures is the phase perturbations introduced by the thermal convection currents flowing around the specimen. Thermal currents change the refractive index of the air surrounding the specimen and hence introduce phase changes in the laser beam propagating through it. The problem of thermal currents can be overcome by evacuating the oven. In the optical configuration shown in Figure 1, both laser beams pass through the same medium in surrounding the specimen. The relative phase changes due to thermal currents are therefore very small. The phase perturbations due to thermal currents can be minimized by recording several successive images of the fringe pattern and averaging their phase values.

 

Conclusion
Electronic speckle pattern interferometry is an attractive technique for the characterization of materials at elevated temperatures. The technique provides full field displacement and strain information, and it is noninvasive. The use of a video camera to record the images of the test object and a digital image processor to process them enables the visualization of full field displacement fringes in real time. Digital fringe analysis technique yields quantitative information on the displacement and strain fields. The technique is successfully employed for the measurement of thermal expansion coefficient of Haynes alloy No. 25 at high temperatures and to study the material response to static loads at 1,000 ºC (1,832 ºF).

 

Acknowledgments
The research work presented in this paper was carried out while the author was at the Illinois Institute of Technology, Chicago. The financial assistance and encouragement of C.A. Sciammarella is gratefully acknowledged.

 

References
Burch, J.M., and C. Forno, "High Resolution Moiré Photography," Optical Engineering, Vol. 21, 1982, pp. 602-614.

Evensen, D.A., R. Aprahamian, and K.R. Overoye, "Vibration Analysis of Composite Panels at High Temperatures Using Holographic Interferometry," NASA Contract Report 2028, 1972

Jones, R., and C. Wykes, Holographic and Speckle Interferometry, Cambridge University Press, Cambridge, England, 1989.

Kang, B.S.J., F.X. Wang, and QK. Liu, "High Temperature Moiré Interferometry for Use to 550º C," Proceedings of the SEM Fall International Conference on Hologram Interferometry and Speckle Metrology, 1990, pp 457-464.

Lockberg, O.J., J.T. Malmo, and G.A. Slettemoen, "Interferometric Measurements on High Temperature Objects by Electronic Speckle Pattern Interferometry," Applied Optics, Vol. 24, 1985, pp 3167-3172.

Malmo, J.T., O.J. Lockberg, and G.A. Slettemoen, "Interferometric Testing at Very High Temperatures by video Holography (ESPI)," Experimental Mechanics, Vol. 28, 1988, pp 315-321.

Sciammarella, C.A., "The Moiré Method - A Review," Experimental Mechanics, Vol. 22, 1982, pp 418-433.

Sciammarella, C.A., and G. Bhat, "Computer Assisted Techniques to Evaluate Fringe Pattern," Proceedings of the Second International Conference on Photomechanics and Speckle Metrology, SPIE Vol. 1553, 1991, pp. 252-262.

Stetson, K.A., "Speckle Photography Applied to High Temperature Deformation Measurement," Proceedings of the Society of Photo-Optical Instrumentation Engineers, Vol. 370, 1981, pp 270-279.

 

* Strainoptic Technologies, Inc., 108 W. Montgomery Ave., North Wales, PA 19454; (215) 661-0100; fax (215) 661-0100; fax (215) 699-7028; e-mailgbhat@erols.com.

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