REVIEW OF SCIENTIFIC INSTRUMENTS 86, 035111 (2015)

A methodology for high resolution digital image correlation in high temperature experiments Justin Blaber, Benjamin S. Adair, and Antonia Antonioua) The Woodruff School of Mechanical Engineering, 801 Ferst Drive, Atlanta, Georgia 30332, USA

(Received 25 November 2014; accepted 8 March 2015; published online 25 March 2015) We propose a methodology for performing high resolution Digital Image Correlation (DIC) analysis during high-temperature mechanical tests. Specifically, we describe a technique for producing a stable, high-quality pattern on metal surfaces along with a simple optical system that uses a visible-range camera and a long-range microscope. The results are analyzed with a high-quality open-source DIC software developed by us. Using the proposed technique, we successfully acquired high-resolution strain maps of the crack tip field in a nickel superalloy sample at 1000 ◦C. C 2015 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4915345] Thermo-mechanical experiments at high temperatures (>800 ◦C) are often used to characterize materials employed in many critical applications, for example, in aerospace and nuclear industries.1–5 In addition to macroscopic load measurements, it is often desirable to obtain full field strain maps under different loading conditions.6–8 Such maps provide invaluable information about material response and greatly enhance the scientific output of a given experiment. For example, strain maps would be quite useful for identification of deformation mechanisms that operate at high temperatures and so far have only been explored with careful post-situ analysis2 and modeling. One of the most widely used methods for obtaining 2D full field strain measurements is Digital Image Correlation (DIC).9–12 DIC is a non-contact technique that uses image registration algorithms to track deformation of a random pattern pre-imposed on the sample surface within a desired field of view. In recent years, there has been progress towards using DIC in high temperature experiments8,13,14 but several issues remain unresolved. (1) High quality, high resolution pattern that is stable under high temperatures. The tests can require temperatures in excess of 1000 ◦C. While some commercially available paints or oxide particles can withstand such temperatures, their adhesion to the sample surface is compromised over time. This is especially true when the paints are dispersed in very small (5-10 µm) droplets required for high resolution patterns. This degradation crucially limits the data that can be acquired during long duration experiments. Furthermore, a native oxide that frequently forms on the surface of a sample can contribute to delamination and overall degradation of the painted pattern. (2) High resolution image acquisition and analysis. The optics and camera setup need to be well calibrated for such experiments to correct for thermal emission and to obtain high clarity images at the desired field of view.

a)Author to whom correspondence should be addressed. Electronic mail:

[email protected]. Telephone: (404)894-6871. 0034-6748/2015/86(3)/035111/6/$30.00

Several tools have been proposed for this task,15,16 but some require specialized optics such as high-resolution UV camera. In this paper, we outline a protocol that provides a stable, high resolution pattern as well as document the high resolution image acquisition. The technique uses standard visible range cameras, so that existing optical systems for room temperature DIC could be easily adapted to perform high temperature experiments. The acquired images are analyzed with Ncorr, an open source DIC software recently developed by us.17 One of the advantages of Ncorr is the inclusion of additional displacement sites close to the crack tip boundary by using a “backwards” algorithm17,18 as well as adjustment of the sub-window shape and size near boundaries. The material tested was PWA1484, a single crystal nickelbased superalloy.19–21 A single edge notch tension (SENT) specimen with dimensions corresponding to American Society for Testing and Materials (ASTM E647-1322) specifications was prepared using electron discharge machining (EDM). The primary and secondary crystallographic orientation for this specimen can be found in Table I. Sample dimensions for the SENT specimen were 203.2 mm long, 38.1 mm wide, and 2.54 mm thick.19–21 The sample was cyclically loaded (Pmin = 0.17 kN; Pmax ∼ 1.7 kN and R = 0.1) at room temperature until a fatigue crack was initiated. The cyclic experiment continued until the total crack length to sample width ratio was a/W ∼ 0.5, where a is the crack length and W is the sample width. For this sample, the fatigue crack was tilted 9.5◦ with respect to the horizontal axis with crack bifurcation occurring during early stages of the fatigue pre-crack growth. After the fatigue crack initiation, the sample surface was sandblasted with average particle size of 500 µm and subsequently laser etched with an infrared laser engraving system. The laser engraving produced a random pattern of two thousand black dots approximately 50 µm in diameter across a 1 mm by 1 mm area around the crack-tip. We note that the pre-crack path is not affected by the surface patterning procedure since the pre-crack formed before sandblasting and laser engraving the surface. The sample was then preheated

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TABLE I. Nickel alloy primary and secondary orientations.

Material PWA1484

Primary orientation

Deviation (deg)

Secondary orientation

Deviation (deg)

⟨001⟩

7.2

⟨010⟩

36

to 1000 ◦C for 50 min until a stable oxide layer formed on the sample surface. Sandblasting the sample roughens the surface so that the native oxide that forms in the pre-heating cycle instills a gray-scale random pattern. When the oxide layer is initially forming, the surface changes dramatically. However, once formed, it remains relatively consistent for the duration of the experiments performed in this study. The pattern density can be easily controlled by the sandblasted particle and laser dot size. The pattern associated with the oxidation of a roughened surface tends to have light gray/white features and is complementary to the black features produced by the laser patterning. The stability of the surface pattern was verified through two load cycles of ∼20 min each at 1000 ◦C with a minimal load hold and a subsequent loading to 11 kN. The DIC algorithm was used to confirm that the pattern remained unchangeable during the two cycles. This behavior is in marked contrast to high temperature paints which lost adhesion and degraded in color at the temperatures achieved in the experiment. In general, sandblasting can alter a very thin layer near the surface of the material and can impose residual stresses. The depth of the damage layer was found to be on the order of tens of microns for Ni superalloy samples sandblasted with particles 4-5 times greater than in this work.23 While a direct experimental analysis of the magnitude and the influence of the residual stress was not performed in this work, both are expected to be quite small. Indeed, the residual stresses should be considerably smaller than those resulting from shot peening, a considerably more invasive process. Multiple studies show that high compressive residual

stresses developed at the surface of shot peened samples are relaxed after treatment at elevated temperatures.24,25 Moreover, previous analysis of relatively high residual stresses caused by laser etching and specimen machining in nickel based superalloy IN100 at lower temperatures showed that these stresses were too shallow to affect the fatigue crack surface morphology and growth rate.26 Therefore, the patterning procedure is not expected to significantly affect either the curved shape of the crack-front or the crack-tip field. A full experimental investigation of this issue is left to a future study. Finally, we note that in this work, the loads were not high enough to cause the pre-crack to propagate. Figure 1 shows the experimental setup including the loading frame, heating coils, and the optics. The patterned sample was tested in tension using an MTS servo-hydraulic load frame with a 100 kN load cell. The sample was heated to 1000 ◦C, and images of the near-crack tip area were obtained at various loading levels using the methodology described below. Sample was heated using an Ambrell HOTSHOT 3.5 kW induction heater with copper coils wrapped above and below the notch as shown in Fig. 1(b). The temperature of the near center region is measured using a thermocouple that is attached at the back of the sample near the sample mid-section. Two fans near the sample area were used to facilitate air flow and reduce heat haze. The heating coils are separated by a 25-30 mm gap to allow the notch to be properly imaged while undergoing deformation. The sample was first equilibrated at 1000 ◦C under a nominal load of ∼0.22 kN and a reference image was obtained. A series of current (deformed) images were obtained with increasing load. A 16-bit SBIG 8300M camera with a high quality fullframe CCD sensor (Kodak KAF-8300) and 3326 × 2504 pixel resolution was used for image acquisition. The camera was attached to a Questar QM-100 long distance microscope (LDM) that allowed for a large magnification (5 mm field of view) to be obtained from a large working distance

FIG. 1. (a) Experimental setup for a high temperature (HT) experiment of a single crystal nickel alloy SENT sample. An MTS testing frame is used to apply the load, and during testing, the images are recorded using an SBIG 8300M camera with a 452 nm bandpass filter attached to a Questar QM-100 long distance microscope. (b) Copper coils are used to heat up the SENT sample.

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FIG. 2. (a) Histograms of images (b) and (c) obtained at 1000 ◦C under nominal load. Image was obtained with (b) bandpass filter and blue light source. Image (c) was obtained with bandpass filter only.

(∼380 mm). The large working distance maintains the integrity of the optics while working at high temperatures. In order to suppress thermal emission from the heated sample, a combination of a blue bandpass filter and a blue light source was utilized.8,13 The bandpass filter placed between the microscope and the camera was a 452 nm TechSpec filter from Edmund Optics. A high intensity blue light emitting diode (LED) (470 nm) spotlight from Edmund Optics (65 mm

coverage at 300 mm working distance) was used to illuminate the sample. Both the dominant wavelength and the intensity of thermal emission depend on the temperature T. For example, for an emitter that is in thermal equilibrium with its radiation (black body radiation), the total intensity increases according to the Stefan–Boltzmann law as T 4, while the dominant wavelength decreases as 1/T (Wien displacement law). At 1000 ◦C, the peak wavelength in the black body spectrum is in the infrared range at λmax ∼ 2.3 µm. While the spectrum of the thermal emission from the sample was not measured directly, the black body spectrum provides a reasonable guidance on the choice of filter. Figure 2(a) shows two histograms of the crack tip region of the sample at 1000 ◦C with and without the blue light, which are shown for images seen in Figs. 2(b) and 2(c), respectively. Figures 2(b) and 2(c) were obtained with the bandpass filter. Images without bandpass filter (not shown) were completely saturated at 1000 ◦C for even the shortest exposure time available. A comparison of the two histograms shows that

FIG. 4. A representative subset in regions (a) and (b), respectively.

TABLE II. Least squares correlation coefficient values obtained for subsets in regions A and B.

FIG. 3. (a) Reference image obtained at a load of F = 0.22 kN and (b) current image at F = 11 kN of the region near the crack tip while the sample is at 1000 ◦C. Region A is an area with both sandblasted and laser patterned dots whereas region B only has a pattern from the sandblasted dots.

Subset

CLS

Region A Region B

0.0363 0.0422

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FIG. 5. ROI construction using the current configuration so that the crack is visibly opened and the ROI can be easily traced so as to exclude the crack. Subsets that are in direct contact with the crack tip boundary are included in the analysis.

the bandpass filter/blue light image has a shift towards darker tones and has a slightly better dynamic range as the image obtained without the blue light. The main difference between the two images is that the exposure with the blue light was obtained in 0.5 s whereas the image without the blue light (Fig. 2(b)) was obtained in 8 s. This order of magnitude change in the exposure time required to acquire an image can be crucial in experiments where long hold times can lead to changes in the sample (e.g., creep, softening) or in the testing frame. Figure 3 shows the near crack tip region at 1000 ◦C at 0.22 kN and after loading at 11 kN. Both images were obtained using the bandpass filter and the blue light (exposure time of 0.5 s). The notch area is clearly visible in both the loaded and unloaded images but the fatigue crack emanating from the notch is only visible in Fig. 3(b), after loading. The region of interest (ROI) contains two distinct patterns: Region A contains a combination of sandblasted and laser patterned dots whereas region B contains only sandblasted dots. Two representative subsets of regions A and B are shown in Fig. 4. The density of the laser speckled dots is relatively low so the subset window diameter is chosen so that it contains at least 2-3 black laser dots. A comparison between the cross correlation coefficients of subsets within regions A and B is shown in Table II. While the resulting black laser pattern is sparse, it has an impact on the overall measurements as

seen by the cross correlation coefficient where a smaller value indicates a better match. We note that the overall quality and intensity of the sandblasted and laser dot pattern did not diminish after three heating and cooling cycles that lasted on average 1 h each. In-plane deformation maps were obtained by further analysis of a reference (unloaded) image and a current (deformed) image. This analysis of the high temperature datasets was done using Ncorr17 and employed the Eulerian to Lagrangian conversion algorithm. The conversion algorithm enables the inclusion of subwindows (subsets) in direct contact with the crack tip that is not typically included when standard DIC algorithms are employed. In order to achieve this, the ROI is defined in the deformed configuration by constructing a mask using any image editing software (e.g., Image J27). The mask is then used to exclude data points within the crack, as shown in Fig. 5. This is a crucial aspect of the algorithm since the crack is clearly visible in the current configuration. From such analysis, the displacement fields are with respect to the current configuration (Eulerian) and the displacements with respect to the reference configuration (Lagrangian) can be obtained. In addition, a subset truncation method was employed to prevent the wrapping of subsets around the crack tip where displacements are highly nonlinear and incorrectly defined

FIG. 6. Lagrangian displacements along the (a) X and (b) Y directions. The in-plane Lagrangian strain components: (c) EYY, (d) EXX, and (e) EXY.

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FIG. 7. Sector distribution around crack tip. Crack is oriented at a 9.5◦ angle with the horizontal. All angles are with respect to the crack orientation angle. The bottom sector is offset from the crack tip edge.

subsets can lead to non-convergence/erroneous results.17 The subset truncation method is also employed in the plane fits of the displacement field so as to obtain displacement gradients and subsequently Green-Lagrangian strains. Figure 6 shows the main results of the analysis with the top row displaying the Lagrangian displacement fields (U and V components) while the bottom row displays the

Rev. Sci. Instrum. 86, 035111 (2015)

resulting Green-Lagrangian strain fields (from left to right, respectively). Simulations and ex-situ SEM analysis suggest that in single crystal nickel superalloys, the strain field ahead of the crack tip is strongly anisotropic.28–30 To the best of our knowledge, the crack-tip field in such system has not been observed yet in-situ with sufficient resolution even at room temperature, let alone in high temperature experiments. Figure 7 demonstrates clearly visible sectors in the strain field. Note the formation of the discrete sectors and their evolution during loading has been predicted theoretically (e.g., Ref. 31). The quantitative information provided by the described experiment could be used to verify existing models. One of the advantages of Ncorr is the ability to define the subset window shape and size so as to exclude any interaction it may have with the crack tip boundary shape. Figure 8 shows the subset truncation effect on the displacements and strains. The subsets in Ncorr are circular and contiguous, so subsets formed near the crack tip can wrap around it as long as the crack tip is within a radius distance of the center point of the subset. This is a problem because the deformation near the crack tip is highly nonlinear, yet the subsets are restricted to first order affine transformations. Subset truncation resolves this issue by preventing the subset from wrapping around the crack tip. The results shown in Fig. 8(b) demonstrate

FIG. 8. Comparison of U displacements ((a) and (b)) and EYY ((c) and (d)) with and without truncation. Distortions near the crack tip (white arrow) are ameliorated through the subset truncation technique. When a subset is in contact with a boundary, the subset size shape is different for the (e) truncation or (f) without truncation.

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that the contours are perpendicular to the boundary and also eliminate the distortions. A similar effect is shown for strain components. The difference between the subset size shape without and with subset truncation is seen in Figs. 8(e) and 8(f), respectively. The subset truncation technique improves the resolution of displacements and strains near the crack tip. To summarize, this paper describes a robust and easily adaptable technique to performing high temperature, high resolution DIC measurements. We described a methodology for (1) obtaining a stable, high quality pattern on the surface by sandblasting and laser dot printing; (2) using a standard optical system with a bandpass filter and blue light for image acquisition at elevated temperatures; (3) data analysis with an opensource 2D DIC code Ncorr. The software enables the analysis near the crack tip while accounting for subset distortions by correcting crack tip or subset size interactions. The reliable pattern is the key to enabling acquisition of high quality images at high temperatures. While some high temperature paints do provide adequate initial adhesion to the sample and could withstand high temperatures, the colors of small speckles tend to fade at higher temperatures thus significantly degrading the pattern and quality of DIC maps. In contrast, the sandblasting and laser patterning techniques have proven controllable and stable. Furthermore, preheating of the specimen to pre-form an oxide layer was found to be beneficial. We demonstrated the utility of the overall approach by performing DIC analysis near a crack-tip during a single edge notched tension test on a single crystal nickel superalloy at 1000 ◦C. This work has been partially supported by the National Science Foundation (NSF) Graduate Research Fellowship under Grant No. DGE-1148903 and an NSF CAREER award, NSF Grant No. CMMI-1351705. A.A. gratefully acknowledges fruitful discussions with Dr. A. F. Bastawros, who first suggested using sandblasting for patterning. The experiments summarized in this paper were performed at the Mechanical Properties Research Lab at Georgia Tech. 1M. Abdou, P. Gierszewski, M. Tillack, M. Nakagawa, J. Reimann, D. Sze, J.

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A methodology for high resolution digital image correlation in high temperature experiments.

We propose a methodology for performing high resolution Digital Image Correlation (DIC) analysis during high-temperature mechanical tests. Specificall...
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