3D Image Correlation: Measuring Displacement and Surface Strain

3D image correlation can be used for rapid full-field strain measurement in the test lab for tensile and fatigue testing and is robust enough for hostile-environment field tests. It requires minimal preparation and provides the results of 10,000 contiguous strain gauges; a capability that is particularly appropriate for composite and ultralight structures. The technique can also be used for measurements in extreme environments, such as temperatures above 1000°C, wind tunnel tests, in engine test cells, and for free-space modal conditions for remote applications.

Full-field optical measuring techniques such as moiré and holographic interferometry are increasingly being relegated to specific measurements for development and design tools and for production inspection. A variety of commercially available optical inspection systems combine increasingly powerful computers, high-resolution digital cameras, and compact mechanical design to provide turnkey operation for engineering measurements.

At the risk of preaching to the converted, it is worthwhile to summarize the advantages of full-field measurements. A single-point gauge cannot show strain gradients and misses unpredicted hot spots, especially with nonhomogeneous and anisotropic materials. Optical measurement results are directly compatible with finite element analysis software and facilitate verification and iteration of these models. Reducing the number of required prototypes and providing a quicker time to market and improved product quality at lower cost are some of the compelling justifications. Perhaps most importantly, measurements that would otherwise be impossible become feasible, opening new avenues of material and structural investigation.

Principles of Operation
A pair of high-resolution metrology CCD cameras views the object under test. 3D image correlation is a combination of two-camera image correlation and photogrammetry and involves applying a random or regular pattern with good contrast to the surface of the test object. The pattern then deforms along with the object and the structure's deformation under different load conditions is recorded by the cameras and evaluated. Initial image processing defines unique correlation areas known as macroimage facets, typically 11–25 pixels square, across the entire imaging area. The center of each facet is a measurement point that can be thought of as an extensometer and strain rosette. These facets are tracked in each successive image with micro-pixel accuracy. Then, using photogrammetric principles, the 3D coordinates of the entire surface of the specimen are calculated. The results are the 3D shape of the component, the 3D displacements, and the plane strain tensor. Figure 1 shows an example of a commercial image correlation system configured for 3D measurement during a tension test. The rigid camera bar is mounted to a tripod that can be placed in front of the test sample at the correct working distance for the part to be in focus and within the measurement volume. Because rigid body motion has no effect on the measurements, this type of setup is adequate for use with servo-hydraulic machines as well as electric screw models. Now let's examine several applications to see how the technique is used.

Figure 1. 3D image correlation camera bar on a tripod, ready for measuring at a load frame. Since rigid body motion is not an issue, the same setup can be used with servo-hydraulic test machines and 3D parts such as the dog bone in the full screen example

High-Temperature Measurement
Since 3D image correlation is a fully optical noncontact method, it can operate in hazardous environments. For instance, we can make accurate high-temperature measurements through oven windows or in open air. As long as the environment does not directly affect the cameras, they maintain their calibration and are accurate; the light is unaffected. We have achieved deformation and strain measurements up to 1400°C, performed daily high-precision thermal expansion measurements of low-CTE (coefficient of thermal expansion) ceramics to 1000°C, and acquired precision measurements in the blast of a jet engine thrust on a field test stand.

To illustrate, we heated an advanced bi-metallic component via induction heating. Figure 2 shows the shape of the part and the strains from the tensile and thermal loads at a temperature of 1000°C.

Figure 2. 1000°C inductive heating of a bi-metallic cylindrical specimen showing the specimen (A) and the resulting image (B)

Click for larger images Figure 3. Thermal loading of a titanium test panel in the thrust of a jet engine (A) shows the warm-up, run, and cooldown (B) (Click image for larger version)
This method is regularly used through oven windows; the oven window becomes part of the optical system and needs to be part of the system during calibration. Likewise, we can measure material deformation and strain in a jet engine thrust (Figure 3). The key requirement for operation in a hazardous environment is that the material's surface coating must be able to survive the environment. High-temperature paints to 2500°F are readily available.

Thin Film, Tissues, and Artificial Muscles
Dielectric elastomers are currently being developed as alternatives to shape memory alloys, piezoelectrics, Terfenol, and other such materials. These elastomers must meet the criteria for high elastic strain, low power dissipation, wide operating temperature range, and rapid actuation with precise control. 3D image correlation photogrammetry is an excellent tool for evaluating the performance of these thin-film actuators.

Figure 4 is a strain map from a circular actuator consisting of a pre-tensioned acrylic substrate with compliant carbon-based electrodes on each side.

Figure 4. Full-field graphic showing range of tensile and compressive strains in the X direction

Under an applied high voltage, the circle rapidly grows in diameter. The section line (Figure 5) indicates the strain profile across the diameter of the actuator and surrounding substrate.

Figure 5. Section line plot shows strain profile across the diameter of the actuator and substrate

A transparent overlay of the strain map onto the corresponding live camera image (Figure 6) shows that the left 20% edge of the actuator was dead (inactive), later determined to be due to misaligned electrodes. Prior to this test, the error was unknown.

Figure 6. Overlay of strain plot on the corresponding live image. Note that the left edge of the actuator was inactive, possibly due to misaligned electrodes during fabrication

3D image correlation enables other types of measurements for actuator development, e.g., determining the hysteresis of linear actuators that may have 10 mm of travel. Wide dynamic range is crucial for this type of application. We can track and quantify rigid body motions such as the end of an actuator and combine the camera shutter sync output with excitation voltages to determine hysteresis over numerous complete cycles, at very high data acquisition rates. On the F-22 military aircraft program, fatigue studies of the wing root and landing gear over many years will help define maintenance schedules. With a high-speed camera setup, we can characterize high-frequency devices such as loudspeaker membranes, study material ballistic response for defensive materials, and study biomechanics during automotive crash studies.

Dynamic Deformation Measurements
The robustness of this technique becomes clearest when we consider dynamic deformations. Using a variety of high-speed cameras, we can capture high-speed events, such as those for ballistic, blast, and crash studies. Furthermore, by adding a precision triggering module and stroboscopic illumination to standard "static" cameras, we can apply the system to nonstationary responses and rotating objects, such as tires, turbo machinery, and jet engine components, as we can see in the following examples.

Click for larger images Figure 7. Ballistic impact result of 3D displacement and strain, collecting 10,000 frames/s (above). Graphs of some of the analysis performed on this aerospace composite sample show out-of-plane displacement on the left and time history on the right (Click image for larger version)
Ballistic Impact. The typical ballistic result in Figure 7 shows the 3D shape of the impact at 10,000 frames/s (7A). The section line (7B) shows how the displacement develops across the sample, while the point plot (7C) is a time history of one point through all of the collected images. To give you a sense of the immense amount of data collected, there are about 5000 curves like this one available for each shot! Any and all data can be exported to MatLab or other external analysis programs for model and simulation verification and validation. NASA chose this method for its critical LS-DYNA model validation, required for the return-to-flight of the space shuttle.

High-Speed Fracture Mechanics. We can also perform high-speed materials studies from fracture mechanics to production-rate forming limit analysis. Systems with fully integrated cameras (500–500,000 frames/s) allow frame cropping to significantly increase the frame rate. By supporting a variety of camera models, users who may already own a single high-speed camera can implement full 3D capability by acquiring a second one together with 3D image correlation software.

We prepared a notched rubber dog-bone specimen and then rapidly stretched it as shown in Figure 8.

Figure 8. Result showing 125% strain as the rubber stretched, using the initial un-deformed image for reference.

By reducing the number of active pixels, we can increase frame rates above the 1000 frames/s at full 1024 x 1024 pixel resolution. In this case, with 512 x 256 pixels, there were 7400 frames/s, meaning that the inter-frame time was 135 μs. Figure 9 is a very small subset of the 250 captured images.

Figure 9. Sequence of captured images showing large deformations from rapid tensile loading

Figure 10. Yellow X's show the measurement points for this test overlaid onto the part
In Figure 10, a strain map is seen together with a live camera image that also shows the center of each facet, or virtual strain rosette. Note that the much higher spatial resolution of the strain field at the crack tip could have been obtained with a closer camera view or increased facet overlapping.

High-Speed Tire Dynamometer Testing. For dynamic events such as a rotating tire, the shortest shutter times may not be adequate to prevent smearing of the applied pattern during the exposure, in which case pulsed illumination is required. For this particular test we used a pulsed arc discharge light configured for a 500 ns discharge time. Figure 11 shows the image correlation setup together with the tripod-mounted arc light and expansion optics.

Figure 11. Here the system is set up to study a tire at speeds up to 290 km/h. For related work such as flywheel testing, rotational speeds of 20–30,000 rpm can be achieved using short-duration (~5–20 ns) laser pulses

A slip ring encoder on the road wheel generated an index pulse once per rotation, which was fed to our pulse/delay generator. By varying the time delay, we could control the rotational position of the tire and synchronize it to the pulsed illumination.

Figure 12 shows the principal strains on the complete tire, indicating a standing wave with highest amplitude near the load area. The result, calculated from a reference condition of 3 mph, shows the evolution of a standing wave pattern near the load area as speed increased. Note that the software can calculate strains between any two measurement conditions, and that additional images (measurement conditions) can be added to a measurement series. For instance, we could import a reference image of the unloaded tire and then recalculate strains relative to this new reference point, if so desired. Alternatively, we can calculate the relative strain between any two intermediate steps in a long measurement sequence in addition to the automatically calculated strains relative to the first step.

Figure 12. Principal strains on the tire at high speed, indicating a standing wave that has maximum amplitude at the load area

Ultra-High-Speed Spin-Pit Testing. Spin testing is an essential step in preventing centrifugal burst. All developers and manufacturers of turbomachinery components need to test for centrifugal strength to verify stress analysis and establish fatigue lifetimes. In particular, they want to monitor the formation and evolution of local strain anomalies. We tested how well pulsed-image correlation could capture "snapshots" of strain behavior during normal testing operations.

As a proof-of-concept test, we used a composite flywheel with a flat surface and measured the in-plane strains using 2D image correlation. This uses a single camera and is sensitive only to in-plane strains; any out-of-plane motion will cause errors in the strains due to magnification changes in the applied pattern. This high-speed, rotating test part would experience no such out-of-plane movement, and the greatly simplified test setup used a single camera mounted in the spin pit.

Figure 13 shows the image correlation camera mounted on the spin pit cover, before insertion into the containment vessel. To protect the camera in the event of a flywheel burst, it was mounted in a massive steel cylinder with a thick polycarbonate viewing window. A pulsed YAG laser reduced the exposure time for each image acquisition to 6 ns, eliminating any smearing of the pattern at high speeds and allowing us to use a standard 20 frame/s camera.

Figure 13. Image correlation camera in an armored housing on a bracket, aimed at a prepared area of interest on the composite flywheel with a possible crack indication

A once-per-revolution signal from a tachometer provided the input to a precision trigger module, which opened the camera shutter within 5 μs. A sync output signal from the camera shutter was delayed, and then output to trigger the pulsed laser. By varying this delay, the laser pulse could be synchronized to any rotation position on the disk as it passed the camera field of view. Figure 14 shows the radial strain measured at 35,000 rpm.

Figure 14. Radial strain result at 35,000 rpm, showing significant banding effects and a maximum radial strain of 5,797 microstrain

In Closing
3D image correlation photogrammetry is a powerful tool for dynamic displacement and strain analysis, providing full-field results with extensive quantitative analysis capability. It can capture operational effects as easily as shooting a video, and using precision synchronization, it can capture peak strains during cyclic fatigue tests.

Synchronized flash illumination extends the applicability of 3D image correlation to high-speed rotating components. Microsecond illumination with Xenon flash and spark-gap sources enables testing on dynamometers at hundreds or thousands of rpm, while nanosecond illumination with a pulsed laser facilitates strain measurements during spin-pit testing on very high-speed rotating components. An 18 in. dia. flywheel rotating at 35,000 rpm was well within the dynamic capability of the system. We see no intrinsic obstacles to extending these measurements to 3D objects, such as bladed disk assemblies by using a pair of cameras.

2D or 3D image correlation photogrammetry can also be combined with high-speed cameras, adding quantitative shape, displacement, and strain measurements to existing analyses for impact studies and other high-speed events. Beyond the camera types shown, you can use double-shot and image-intensified cameras with 10 ns interframe and exposure times.

Further Reading

  1. Cloud, Gary, Optical Methods of Engineering Analysis, Cambridge University Press, 1995.
  2. Williams, D.C., Ed., Optical Methods in Engineering Metrology, Chapman and Hall, 1993.
  3. Tyson, J., "Noncontact Full-Field Strain Measurement With 3D ESPI," Sensors, Vol. 17 No. 5, pp. 62–70, May 2000.
  4. Mikhail, E., Bethel, J., and McGlone, J., Introduction to Modern Photogrammetry, John Wiley and Sons, 2001.
  5. Shahinpoor, Mohsen, and Kim, Kwang J., "Ionic polymer-metal composites: I. Fundamentals," SMART Materials and Structures, Volume 10, pp. 819–833, 2001.
  6. Tyson, Schmidt, and Galanulis, "Biomechanics Deformation and Strain Measurements With 3D Image Correlation," Photogrammetry, Experimental Techniques, Vol 26 No. 5, pp. 39–42, Sept/Oct 2002.
  7. Schmidt, Tyson, and Galanulis, "Full-Field Dynamic Displacement and Strain Measurement Using Advanced 3D Image Correlation Photogrammetry," Experimental Techniques, Part I: May/June 2003, Vol. 27 No. 3, pp. 47–50, Part II: May/June 2003, Vol. 27 No. 4, pp. 44–47.

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