Simcenter Testing Solutions Digital Image Correlation for Static Testing

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Digital Image Correlation, commonly referred to as DIC, is an optical measurement technique that uses images from digital cameras to determine complex shapes, displacement, and deformation fields at the surface of objects under any kind of loading.

An example DIC measurement of a material characterization test under static load is shown in Figure 1.
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Figure 1: A material coupon (speckled, center) is subjected to a tensile static load to determine its elastic and plastic properties.

This article is an introduction to Digital Image Correlation for static testing. It has the following contents:

1.    Introduction of Digital Image Correlation (DIC)
2.    Basic Concepts of Digital Image Correlation
   2.1 Components of a DIC Test Setup
   2.2 Pixels and Speckle Tracking
   2.3 Camera Configurations
   2.4 Test Setup Calibration
3.    Quasi-static testing
   3.1    Strain Measurements
   3.2    Material Property Characterization
4.    DIC Application cases
   4.1 Concrete
   4.2 Composites
   4.3 Metals
   4.4 Foams
   4.5 Thin Films
   4.6 High-speed Transients
   4.7 High Temperature
   4.8 Rotating Machinery
5.    Conclusions

1. Introduction of Digital Image Correlation (DIC)

The genesis of Digital Image Correlation (DIC) is from the 1970 s when cross-correlation techniques were used to measure the shift of pixels used in a digital image. As digital photography has evolved, DIC has been used progressively and more extensively since the early 1980 s in quasi-static testing scenarios for material characterization, structural validation and fracture mechanics.  This is due to its ability to provide a full field view on the deformation pattern of the structure at given instances in time. 

Another benefit of this technique is the ability to capture accurate geometry for metrology applications which can also be used for topology validation.

Thanks to recent advances in camera technologies (speed and resolution), processing power and more efficient algorithms, it has become possible to also measure highly dynamic responses and vibrations, which has raised a lot of interest in the structural dynamic's community. Digital Image Correlation has promise to be a game changer with regards to techniques of modal testing.

DIC is a non-contact method, and using the high-resolution digital photography will allow test data to be aligned closer to the Finite Element models, bringing a paradigm shift in the fidelity available for model validation, and getting us closer to the Digital Twin model than ever has been possible before. An example of this using a scaled model of an aircraft for a dynamic s application is shown in Figure 2.
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Figure 2: The modal results from a test of a scale airplane are shown on the left, and its Digital Twin simulation mode shape is shown on the right. The mode shape is the first wing bending mode.

The intention of this first article is to give an overview of the DIC technology and basic concepts in the context of static testing. 

2.    Basic Concepts of Digital Image Correlation

In a Digital Image Correlation test, cameras are used to create a series of images of the test article to measure its deformation. The process is outlined in Figure 3 below.

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Figure 3: The Digital Image Correlation (DIC) process starts with applying a speckled paint pattern to a test object (left), acquiring images of the test object deformation (middle), and then processing the images to determine deformation or mode shapes (right).
After a test article is prepared properly (by applying a speckle pattern), a series of images are collected as the test article is loaded or deformed.  These images are then processed into strains and/or displacements.  Deflection patterns and mode shapes can also be processed from the images.

2.1 Components of a DIC Test Setup

The fundamental components ( Figure 4) of a DIC test setup vary depending if two dimensional (2D) motion or three dimensional (3D) motion is to be measured:
  • Two Dimensional: For 2D planar measurements only one camera is needed, but it must be mounted perfectly perpendicular to the object. Any kind of out-of-plane or rigid motion will negatively affect the accuracy of the results, so this method is typically only used in very few applications.
  • Three Dimensional: To provide a depth of field for 3D out-of-plane measurements, two cameras in stereo configuration are used. In this way the system works just like a pair of human eyes.
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Figure 4: To create a deflection image (lower middle), a Digital Image Correlation (DIC) system includes cameras (left, purple), speckled test article (middle, orange), and software (right, blue).

Another component required is a good lighting system to illuminate the test item. This provides the needed contrast in the image to track the variations in small speckle patterns which are naturally part of the surface or artificially applied. The principle behind the DIC process is in tracking this pattern of speckles that are adhered to the surface of the test item using the pixels of the camera.

2.2 Pixels and Speckle Tracking 

Pixels are a fundamental unit of digital images. The cameras that are used for this application works with black-and-white images and use typically pixels that are made up of 8-bits (1-byte) of digital information. This provides a range of 256 gray scale levels. The pixels can be used to track the color variations as the speckles move using a correlation algorithm. The speckles will deflect for example from some applied load. Since the color variations are being tracked between subsequent images, there needs to be some contrast in the image. This is done through a random speckle pattern as shown in Figure 5.
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Figure 5: By zooming in on a portion of the speckle on the left, the pixelization of the digital image can be seen on the right.
Zooming into the image can show the individual pixels that make up the image. As mentioned, if there is not a natural speckle pattern and contrast between the surface points, then this must be applied artificially. This can be done in a few different ways. Using spray paint, or an adhesive paper are 2 possibilities. If there is a natural speckle pattern inherent in the material, then this can be used. The number of pixels that are contained in a digital image and used for tracking the speckles is determined by the camera resolution. The max resolution of the common cameras used can vary from about 1Mpixel to 30Mpixel. This gives 1 to 30 million data points in each image. A 5Mpixel camera is commonly used in these applications. 

By taking a series of images, a group of speckles within a small area can be tracked. These small groups of speckles are called Subsets and a number of these subsets are part of the test setup. A software algorithm will track the position of the unique speckles contained in the subsets.  By doing so, the relative displacement of the speckles within the subset can be determined, which represents the 3D motion of the subset. For example, as shown in Figure 6, as the load is applied, the material stretches, and the subsets are tracked. The displacements of each subset can also be tracked relative to all other subsets. The number of subsets is unlimited and can even be represented as points from a Finite Element (FE) model mesh, which leads to a direct comparison of an FE model under load. 

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Figure 6: By tracking over time (T1, T2, etc) a group of speckles (subset in red square), the relative displacements in three dimensions can be determined.

The subsets are used to cover the Area of Interest , (AOI). The density and number of these subsets is a variable in the software and is also determined by the Stepsize . With this 3D deformation information of each subset, then engineering strain can be calculated. With many images and including time information, Vibration data can also be determined.

As part of the DIC processing setup, some information must be provided to the algorithm. Some of the most important parameters are described in Figure 7.
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Figure 7: The terms "Area of Interest", "Subset", and "Stepsize" which are used in Digital Image Correlation are shown.
The DIC processing will track all speckle points in the field of view of the cameras and in a designated area of interest. Therefore, it is designated as a Full-Field measurement technique, as opposed to a discrete point measurement like with a strain gage or accelerometer. With one camera, an only two dimensional (2D) displacement in the field of view can be tracked. Adding a second camera allows depth perception to track displacements in three dimensions (3D).

The camera hardware has an influence on the results that can be obtained. For example, the frame rate will determine the time step from one image to the next which determines the jump in time of the temporal resolution of measured displacements. A typical camera will vary from a few frames per second (fps) to higher than 1000fps. The timestamp of the images gives temporal information, meaning the displacement as a function of time can be derived.  The displacement data can also be converted to velocity and acceleration information for dynamic measurements.

This gives full-field quantification of displacements in the camera view and includes information in all directions. This can give spatial information giving strain data, and temporal information including velocities and accelerations, or a combined effect can give strain rates. All of this can be obtained from a single test! An example of multiple images acquired with temporal information is shown in Figure 8.

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Figure 8: Setup of a test specimen under load at different times (T1, T2, etc). The timestamp (T1, T2, etc.) of each image provides the temporal information so that displacements can be converted to other values related to time such as strain rates, velocity, and accelerations.

The corresponding full-field animation is shown in Figure 9.
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Figure 9: Full-field strain deformation of a test coupon.
Through a calibration process, which will be described later in this article, very accurate geometry information can be generated and exported into a stereolithography file (.stl) file, excel spreadsheets, or Universal File Formats. This can be used in Finite Element Analysis (FEA) model calibration or animation of the processed data.

In summary, the information that can be derived from a DIC test includes:
  • Full-field 3D displacement data
  • Metrology information
  • Strain Field and Strain rates
  • Velocities & Accelerations

2.3 Camera Configurations

Depending on the situation and objectives of a test, there can be different camera arrangements that are possible, as shown in Figure 10
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Figure 10: Multiple DIC arrangements are possible depending on the test objectives and circumstances.
2.4 Test Setup Calibration 

There are a lot of details as part of the setup process, which are beyond the scope of this article, but an important step in the process is the calibration of the setup. The goals of the calibration process are to:
  • Determine the orientation of each camera relative to each other
  • Determine the orientation in space of each camera relative to the test object
  • Determine the scale for converting the geometry and deformation information into engineering units
  • Establish a local and global coordinate system
  • Determine and quantify any optical distortions
The calibration is done by using calibration plates which have a very precise geometrical grid and oriented relative to a set of fiducial points that are stamped onto the plates. By providing this geometry information to the calibration algorithm and using many images from different orientations of the calibration plates moving within the camera view, the internal camera pixel geometry can be used to determine the results of the calibration process. With standard calibration plates, the geometry information can be automatically entered into the calibration processing by scanning the QR code stamped onto the plates.

For the Multi-camera configuration there must be images which are overlapping from one set of cameras to the adjacent camera set. There can be many calibration images taken which range from 10 to 50 or more images. The more images taken then the more accurate is the information obtained from the process, but of course there is a limit in accuracy that is needed. Using the images and a triangulation scheme for processing the data, the calibration information is obtained very efficiently. Some examples of the calibration images are shown in Figure 11
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Figure 11: Calibration images are taken with a calibration plate that have points on the plate at very precisely located points. The geometric locations of these points can be automatically provided to the calibration algorithm. Using multiple images, the plate is reoriented within the field-of-view (FOV) of the camera. 
A schematic of the calibration process and results is shown in Figure 12.
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Figure 12: Using a Triangulation scheme to process the images of the calibration plates, the calibration process will calculate relative geometry information for the coordinate systems of all components in the DIC test setup.
The goal of the calibration is to relate the camera image(s) to absolute displacement of the test article or part.  It can be thought of as relating the local frame of reference of individual camera(s) to the global frame of reference of the test object.
3. Quasi-Static Testing

Digital Image Correlation can be used for the traditional quasi-static applications of strain measurements and material property characterization. The DIC technology has been grounded in this application and extensively used since the early 1980 s.

3.1 Strain measurements

DIC has certain advantages over traditional measurement techniques like strain gage measurements provide only an average strain ( Figure 13) over a given area.
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Figure 13: Strain is the change in length of an object divided by the original length.

When using a single-point strain gage to measure strain over a given area, there must be some modeling or engineering judgement about where to place a strain gage, as shown in Figure 14. The accuracy is then dependent on the quality of the modeling, or the person making the determination. How to know if the gauge is mounted on the Hot Spot where strain is most concentrated?
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Figure 14: The location of the strain gage may be at the point of maximum stress concentration, but what if it is not? How to know?
Reliance on accurate placement of strain gauges is less of a consideration with DIC methods. Because DIC is a "full field" method, strain is calculated and measured in all areas of the structure visible to the cameras.

An important parameter to use as input to a finite element model for accurate load estimations is the Elasticity Modulus (E) or Young's Modulus, which relates the material stress to strain. There are methods to measure this quantity such as an extensometer, which is used to develop the stress/strain curve. The slope of the curve determines the value of E. An example of an extensometer is shown in Figure 15.
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Figure 15: An extensometer (green) is used to determine the Modulus of Elasticity of a material, assuming isotropic material properties, by measuring displacement.

Using the extensometer method assumes an isotropic material property. If the material used is predominantly homogeneous like metals, and the measurements are properly applied, then it can be very accurate. However, there are situations where an isotropic assumption is not correct for a given material, for example, a composite. Using the full field strain information, the material properties can be estimated through an accurate measurement of the force and the material cross sectional area. 

With DIC, a strain value can be obtained anywhere on the surface of the material. This can be helpful in also correlating the results from Finite Element Model predictions using what are called Virtual Strain Gages . This allows to verify the methods used in the model prediction, while also validating that the model is producing correct results based on correct modelling. An example of using test results to verify and validate a model are given in Figure 16.
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Figure 16: DIC gives very local information to provide high fidelity results to verify and validate model methods and predictions.
As has been discussed, measuring the strain fields and displaying the strain at certain load levels, or how the strain progresses through a material over time is very helpful to know how a structure will react to operational loads. This information can be used to compare with model predictions so the model can be modified to be more in line with the real-world measurements. One way to do this is to Qualitatively look at the colormap of the results in a dual display, as shown in Figure 17.
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Figure 17: Using the DIC results from data collected on a pressurized airplane panel, a strain map is shown for DIC measurements in the left display. The corresponding model predictions are shown in the right-side display.
However, just comparing the results in this way could lead to wrong assessment: are the differences due to errors in the models or they are introduced in the DIC calculations? DIC is a powerful technique but is also sensitive to the settings used so a more robust approach is needed to ensure the effects of these parameters on the results are accounted for. A solution to this is to allow importing the simulation results into the DIC solution, align the Finite Element (FE) and DIC models, and then apply DIC results directly on the FE model after virtual images have been generated.

By applying the same calculations to FE and experimental images we can ensure that all highlighted differences can be used to improve the accuracy of the model and are not introduced by data processing artifacts. By subtracting the DIC results from the FEA ones, one can obtain a correlation map which immediately shows us the regions where these differences are visible, which will show Quantitatively and more profoundly where there are discrepancies and where the model needs improvements, as shown in Figure 18. The results of this can be used for model refinement which can produce eventually a True Digital Twin of the real structure.
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Figure 18: The quantitative differences between the DIC and FEA results can be accurately displayed. The left side is a planar view and the right side is a skewed view.
A critical evaluation of this Levelling approach is presented in the International Journal for Experimental Mechanics: Validation of finite-element models using full-field experimental data: Levelling finite-element analysis data through a digital image correlation engine by Pascal Lava, Elizabeth M. C. Jones, Lukas Wittevrongel, Fabrice Pierron.

3.2    Material Property Characterization

With more Exotic composite materials being developed, and with the proliferation of Additive Manufacturing (AM), characterizing material properties becomes much more difficult with traditional methods. Other examples where this is true include Hyperelastic Materials and Metal-Matrix Composites which have their own set of challenges. The strain can possibly vary by quite a lot from point to point and this is picked up by the DIC method and not by an extensometer or strain gage measurement, which assumes isotropic behavior and averages the strain over an area. The DIC method can more readily identify hot-spots where the strain may be concentrated. So DIC gives much more local information.

To illustrate this, the example in Figure 19 shows the variation of strain of an additive manufactured material which was produced with Laser Sintering . 
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Figure 19: The strain can vary quite a lot across even a small sample of material. The Full-Field DIC method can measure very accurately across the entire material.
The DIC technique can also be applied to virtually any material surface whereas strain gages are limited in that respect. 

A unique feature of the Simcenter Testlab Digital Image Correlation solution is the Virtual Fields Method (VFM).  The user chooses a material model from an extensive library that best characterizes the sample. An optimization process is then run, with the measured data as input, to identify the model coefficients, (e.g. the Young Modulus, Poisson s Ratio, etc.). Compared to classical approach, which relies on finite element indirect updating techniques, the VFM method has a much faster convergence and does not require hundreds of model evaluations.  

The material properties can then be easily used in Finite Element simulation to better predict the structural behavior of specimens built using the identified material. The process is shown in Figure 20.
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Figure 20: The process to determine material properties with the VFM module is shown here. The final results are used in model refinement.

4.    DIC Application Cases

There are many materials and methods for which DIC can be applied. The next section will provide some examples.

4.1 Concrete

Strain gages are very difficult to apply in applications using concrete. With DIC the strain field can easily be obtained as shown in Figure 21.
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Figure 21: The strain field (right) of concrete beam (left) under load.
Why is concrete difficult for a traditional strain gauge? Concrete is an inhomogeneous material with partial grains and pebbles. Strain gauges that are too short might measure the pebbles (with little deformation) instead of the underlying material. Because DIC is full field, it cannot be "fooled" by individual pebbles in the concrete.

4.2 Composites

Composite materials are not isotropic nor are they homogeneous.  They are composed of different layers with fibers in different orientations.

Traditional methods provide an average strain, but strains can vary quite a lot around the surface. Even if it was possible to apply a strain gage, it will still not give the whole picture of where strain concentrations occur. An example of some DIC results on composite material is shown in Figure 22.
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Figure 22: The strain field of a composite material (left) under load is not uniform nor homogeneous (right).  This strain pattern can be easily missed by individual strain gauge measurements.
As more of these types of exotic materials are being developed, DIC will prove to be the best way to study these material properties.

4.3 Metals

In metal structures, traditional strain gauge methods are acceptable in accuracy, but knowing the exact location to put the strain gage can be difficult. Because DIC gives a full field view of the test object, it helps alleviate the issue of trying to place a few gauges in the correct key locations to measure.  Trying to compensate by measuring many individual strain gauge locations can be prohibitive from a time and cost point of view compared to DIC.

An example showing a metal pipe under load is shown in Figure 23.
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Figure 23: Maximum principal strain deformation (right) of a steel pipeline structure (left) under load.

The time for testing using DIC is comparable to using strain gages, but the information from a DIC test is more extensive.

4.4 Foams

For foam material, attaching a strain gage is not possible. The deformation of foam under compression from a DIC measurement is shown in Figure 24.
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Figure 24: Compressive test deformation (right) on foam material (left).

The strain results from DIC can vary in the way they are presented. In Figure 24 these are shown as Minimum Principal Strains .

4.5 Thin Films

For thin film material the loads can be applied through the elastic region and into the plastic region until almost fracture ( Figure 25).
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Figure 25: Thin film material (left) with load applied (blue arrow) showing deformation into final rupture (right).

In the DIC animation, the progression to ultimate load can be seen.

4.6 High-Speed Transients

Another application for DIC is for high-speed events, using high-speed cameras. The previous discussions were dealing with quasi-static applications. For DIC processing it really does not matter if the images are obtained slowly over time or if the images capture a transient event with medium to high-speed cameras. In all cases the processing is the same, and it just relies on high-quality images with appropriate speckle information. A couple of examples are shown in Figure 26 and Figure 27.

Figure 26 shows the deflections of a pouch as it is dropped. The images are captured with a camera at 5k frames per second (fps).
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Figure 26: High-speed cameras can be used with DIC. The processing is the same for all low and high-speed cases. Having temporal information allows also velocity and acceleration information to be obtained.

The results are presented as acceleration. Since the displacement is a result from DIC, and since the images are time-stamped, then the velocity and accelerations can be obtained too. Obviously, strains are also available when performing high-speed imaging. With ultra-high-speed cameras even ballistic events can be captured.

The example in Figure 27 results from images captured with a camera at 5M frames-per-second (fps).
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Figure 27: Ultra-high speed camera capturing a ballistics event.

The structural wave propagation from the shock event can be tracked with DIC, even if the material experiences plastic deformations. Using traditional measurement sensors would either fail or give erroneous results once a material enters the plastic region, but DIC can be used to detect this condition, and then also track how the responses change due to plastic deformation, which is important for multiple events at high stress levels, and durability applications.

4.7 High-Temperature

Measuring strain for high-temperature applications is possible with DIC. Installing a strain gage on metal and then raising the temperature to red-hot will destroy the sensor. With DIC, by using some special equipment such as a high-intensity blue LED lighting will allow the measurement of an object for high-temperature applications. Samples can be speckled with high temperature paint to add contrast at elevated temperatures. This contrast provides improved deformation tracking. High resolution cameras and high intensity blue LED lighting can be aimed at specimens through the front or rear windows of a test chamber to obtain the images, as shown in Figure 28
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Figure 28: A high-intensity blue LED light is used for high-temperature DIC testing.
An example of the test specimen for the tensile test at high temperature is shown in Figure 29.
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Figure 29: Intense blue LED lighting enables clearer images at high temperature by counteracting the emissivity of the specimen. DIC results are shown on right.
The image to the left shows the specimen at elevated temperature, while on the right it shows the results from the DIC processing. The test specimen was heated to a temperature of 1300degC.
4.8 Rotating Machinery

It has been shown that DIC can also be applied for rotational machinery testing. In this application, a quasi-steady RPM of the small computer fan is imposed and measuring the RPM can be used to synchronize the camera acquisitions. The test setup is shown in Figure 30.
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Figure 30 A DIC test setup showing a computer fan. The test was made to show displacement and strain data and the corresponding operational deflection shapes of the fan with damaged blades.
The rate of the image acquisition and the resulting number of images corresponds to the resolution of rotational angle information. Given an offset angle of 1 degree, there would be 360 total images acquired for processing. The strain field can be evaluated at each rotational angle. There were two cases that were part of the study. The first case had some slight damage to the blade which created small imbalances and the inherent vibration. Figure 31 shows some results.
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Figure 31: The DIC results shown for a damaged blade case.
The second case, as shown in Figure 32, was done by completely removing one whole blade, producing rigid-body response.
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Figure 32: The DIC results with a single fan blade removed.

There is an algorithm built into the software to compensate for Rigid-Body response.

5. Conclusions

Hope this article acts as a good introduction to digital image correlation. More practical DIC measurement information can be found on the International Digital Image Correlation Society (iDICS) web site.  It has an excellent reference guide " A Good Practices Guide for Digital Image Correlation".

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