# Digital Image Correlation

## Objective

One object of this experiment is to explore the displacement and strain behavior of structures using the digital image correlation technique. In addition, you will explore the interesting response of polypropylene, a material that exhibits different moduli in tension and compression. The experiment consists of two tests: 1) a four point bending test of a polypropylene specimen from which you will estimate the elastic moduli of polypropylene; and 2) a tension test of a second polypropylene specimen with a hole cut in it, from which you can determine the strain and stress concentrations caused by the hole. The loading for both tests will be accomplished using an Instron load frame.&#x20;

## Background

### Digital Image Correlation

In the context of structural testing, Digital Image Correlation (DIC) is a method for tracking the point-wise displacements of a structure (typically a surface of the structure) using a series of images of the structure undergoing deformation. DIC is a non-intrusive measurement technique since nothing has to be mounted to the specimen directly. Furthermore, DIC can measure real structural component geometries in real world conditions. The DIC measurements are primarily limited by image resolution, such that higher resolution images produce more accurate results. Alternatively, a higher-resolution displacement field can be captured by zooming the camera’s field of view to a smaller portion of the specimen of interest. To use DIC, it is usually necessary to prepare the specimen by painting a high-contrast speckle pattern on the surface so that subsequent pre- and post-deformation images can be analyzed to accurately determine the displacement field on the structural surface.

There are some requirements and rules-of-thumb for producing good speckle patterns. First, the pattern should be “random”; a highly organized and repeatable pattern would produce ambiguity in the displacement measurement. Second, the size of the speckles (or high contrast objects) should be roughly the same as (or slightly larger than) a 3x3 pixel region on the digital image for optimal tracking of the displacement. If the speckles are smaller than this, the image magnification can be changed to meet this criterion. Finally, the “density” of speckle features should be sufficient to have an average of 3-4 such features in a 10x10 pixel region. DIC does not rely on correlating a single speckle features, but rather multiple features to get an average displacement in a (multi-pixel) sub-region of the image.

DIC has its origin in speckle imaging approaches used in solid mechanics, and correlation-based analysis methods developed in the 1980’s for object tracking in image processing applications and particle-based velocimetry measurements in fluid mechanics. In fact, DIC is very similar to a common velocity-field measurement approach used in fluid mechanics, Particle Image Velocimetry (PIV). In both DIC and PIV, the individual displacements of many small subregions of an imaged area are obtained by comparing images before and after the displacement has occurred. For each subregion, the “before” (pre) and “after” (post) images are cross-correlated, sometimes using Fast Fourier Transform (FFT) algorithms. The displacement for that subregion is the one that provides the best correlatio**n** between the two images. In DIC, the displacement is the desired quantity. In PIV, this displacement is divided by the (short) time between the two images to obtain the local velocity.

This analysis process is typically performed after recording a sequence of images. In DIC, after the displacement field is calculated, the strain field can be determined. The two-dimensional surface displacement field is characterized as _u_(_x_,_y_) and _v_(_x_,_y_), where _u_ and _v_ are the displacements in the x and y directions for a point originally at location (_x_,_y_). With _u_ and _v_ determined, we can obtain the surface strain field using the strain-displacement relationships

$$
\large \varepsilon_x=\frac{\partial u}{\partial x}\qquad\varepsilon_y=\frac{\partial v}{\partial y}\qquad \gamma_{xy}=\frac{\partial u}{\partial y}+\frac{\partial v}{\partial x}
$$

(1)

Note that differentiating the displacement data amplifies the noise in the data; so advanced analysis software like the package used here$$^1$$ employ additional processing approaches such as sophisticated smoothing to find the strain field from the displacement data.$$^2$$

{% hint style="info" %}
$$^1$$In this lab, we will use the Correlated Solutions VIC-2D analysis software package.

$$^2$$You will also export the VIC-2D DIC data so you can analyze the full-field data.
{% endhint %}

![](https://368320314-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F-MIV0GglxIUR4tETuwA2%2Fuploads%2FlvpLp0anCn6VLAp0SAu4%2FDIC.jpg?alt=media\&token=c7e6d592-68fb-459d-939e-e53022d066e7)

> **Figure 1.** The 3D DIC imaging systems, with two cameras mounted in a stereoscopic configurations and two light sources.

DIC (and PIV) systems come in different flavors. For example, the measured displacements of a thin region can be two-dimensional (2D) or three-dimensional (3D). In this lab, we will use a 2D DIC system (shown in Figure 1) that enables us to capture displacements in two coordinate directions, disallowing us to characterize out-of-plane deformations. A 2D system provides more information than the more common 2D systems by adding an additional measurement. The 2D system requires only one camera (or equivalently, only camera imaging view point). To capture out-of-plane deflections, the 3D DIC system uses two cameras in a stereoscopic configuration. It is important to reiterate that 3D DIC (and PIV) systems provide three components of displacement (or velocity) from a surface (or thin planar region). There are also _volumetric_ DIC and PIV approaches that provide 3D results for each location within a three-dimensional volume.

Our 2D DIC system, which employs one 2.7-megapixel camera, will measure the displacements within a test area that is centered on the test specimen. While a 3D DIC system provides accurate 3D displacement fields, it requires additional calibration effort compared to a simple, single-camera 2D system.  Because we are using a 2D system, our calibration will be relatively simple and the VIC-2D software along with this procedure will educate you on how to carry it out.

### Four-Point Flexure Testing

The four-point flexure or bending test is designed to test the flexural response of a slender beam. The goal of the four point bending test is to create a state of pure bending. Pure bending is a stress state where the bending moment is constant and the shear resultant is zero everywhere. The diagram on the left in Figure 2 illustrates a pure bending condition in which only opposing bending moments are applied to either end of the beam. Unfortunately, it is difficult to generate a pure bending moment in a real experiment. Instead, we will use opposing off-set point loads that generate a couple at either end of a beam. This configuration is shown on the right diagram in Figure 2. The advantage of this loading condition is that over the central span there are no shear loads and the beam is subject only to a bending moment.

![](https://368320314-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2Fae3610%2F-MMHuyGav47Xk9URWn6t%2F-MMHxvUUshX5e6MHAVEh%2F16.jpeg?generation=1605562253056013\&alt=media)

> **Figure 2.** Idealized pure bending load (left); four point bending test load (right).

Figure 3 illustrates the setup of the test apparatus for the four point bending test. The test specimen is placed on rollers which are placed below and above the specimen. The load frame applies a compressive load to the experimental apparatus which transmits point loads to the top and bottom of the beam. Rollers are used to ensure that simple support conditions are imposed.

![](https://368320314-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2Fae3610%2F-MMHuyGav47Xk9URWn6t%2F-MMHxvUV43HNPyCAjcUG%2F17.jpeg?generation=1605562253051391\&alt=media)

> **Figure 3**. Apparatus schematic for a four point bending test

**Under ideal conditions in pure bending**, the strain in the beam should be linear through the thickness:

$$
\large \varepsilon_x=-\kappa y
$$

(2)

Furthermore, **if the material is linear elastic and isotropic**, then Hooke's law applies and the bending moment can be calculated as follows:

$$
\large M=-\int_A\sigma_x ydA=-\int_A E\varepsilon_xydA=\int_A E\kappa y^2dA=EI\kappa
$$

(3)

where _I_ is the second moment of area of the beam, which is given as

$$
\large I=\frac{wh^3}{12}
$$

(4)

In Eq. (4), _w_ is the width of the beam, and _h_ is its depth. **Therefore, if we impose** _**M**_ **through a four point bending test, and can estimate from the digital image correlation results, we can infer the elastic modulus** from

$$
E=\frac{M}{I\kappa}
$$

(5)

Polypropylene, however, exhibits different elastic moduli under tension and compression. As a result, the neutral surface is not at the geometric centroid of the cross-section and we have to use a composite beam analysis technique to find the elastic modulus under tension and compression. The measured strain will be offset from the geometric centroid, i.e., Eq. (2) has to be modified as follows:

$$
\large \varepsilon_x=-\kappa y-b
$$

(6)

where _b_ is a strain offset.

The through-thickness stress distribution is shown in Figure 5. The _y_-location of the neutral surface can be found as $$y_N=-b/\kappa$$. The bending moment can be found by a similar integration as that in Eq. (3), except using Eq. (6) for the strain and integrating separately on either side of the neutral surface, i.e.,

$$
\large M=-\int_{-w/2}^{w/2}\int_{-h/2}^{y_N}-E_T(\kappa y^2+by)dydx-\int_{-w/2}^{w/2}\int_{y_N}^{h/2}-E_C(\kappa y^2+by)dydx
$$

(7)

Integrating Eq. (7) yields

$$
\large M=wE_T\left(\kappa\left(\frac{y_N^3}{3}+\frac{h^3}{24}\right)+\frac{b}{2}\left(y_N^2-\frac{h^2}{4}\right)\right)+wE_C\left(\kappa\left(\frac{h^3}{24}-\frac{y_N^3}{3}\right)+\frac{b}{2}\left(\frac{h^2}{4}-y_N^2\right)\right)
$$

(8)

Substituting our expression for $$y_N$$in (8) and simplifying gives

$$
\large M=wE_T\kappa\left(\frac{h^3}{24}+\frac{b^3}{6\kappa^3}-\frac{bh^2}{8\kappa}\right)+wE_C\kappa\left(\frac{h^3}{24}-\frac{b^3}{6\kappa^3}+\frac{bh^2}{8\kappa}\right)
\\ \space \\ \space \\
=\frac{w}{24}E_T\kappa\left(h-\frac{2b}{\kappa}^2\right)\left(h+\frac{b}{\kappa}\right)+\frac{w}{24}E_C\kappa\left(h+\frac{2b}{k}\right)^2\left(h-\frac{b}{\kappa}\right)
$$

(9)

Next, we know from equilibrium that there cannot be an internal axial load in the beam. Therefore, the axial resultant (_N_) must be zero:

$$
\large N=0 =\int\sigma_x dA
\\ \space \\
=\int_{-w/2}^{w/2}\int_{-h/2}^{y_N}-E_T(\kappa y+b)dydx+\int_{-w/2}^{w/2}\int_{y_N}^{h/2}-E_C(\kappa y+b)dydx
$$

(10)

Integrating Eq. (10) and replacing $$y_N$$ with $$-b/\kappa$$ yields

$$
\large 0=E_T\left(\frac{2b}{\kappa}-h\right)^2-E_C\kappa\left(\frac{2b}{\kappa}+h\right)^2
$$

(11)

Now combining Eq. (11) and Eq. (9) for the bending moment, eliminating \_\_$$E_C$$ and using our expression for the 2nd moment of area, Eq. (4), results in

$$
\large M=\frac{wh}{12}E_T\kappa\left(h-\frac{2b}{\kappa}\right)^2=E_T\kappa I\left(1-\frac{2b}{h\kappa}\right)^2
$$

(12)

Eq. (12) can be solved for the modulus under tension, giving

$$
\large E_T=\frac{M}{I\kappa\left(1-\frac{2b}{\kappa h}\right)^2}
$$

(13)

Inserting this into Eq. (11) provides an expression for the compressive modulus

$$
\large E_C=\frac{M}{I\kappa\left(1+\frac{2b}{\kappa h}\right)^2}
$$

(14)

### Stress Concentrations

Stresses around defects and sudden changes in a structure can be significantly higher than the average stress in the structure. These sharp increases in stress are called **stress concentrations**. A good example of a stress concentration is the behavior of the stress near a circular hole in a structure subject to uniform tension or compression. For an infinite plate loaded in-plane, the tangential stress around the edge of the hole has an analytic solution

$$
\large\sigma_{\theta\theta}=\sigma_{av}(1-2\cos2\theta)
$$

(15)

where the coordinate _θ_ runs circumferentially around the circular hole and $$\sigma_{av}$$ is the average stress in the specimen far away from the hole. The direction _θ_=0 is aligned with the loading direction, or the _x_-axis in our geometry. The maximum value of the stress (due to the hole) normalized by $$\sigma_{av}$$ is known as the stress concentration factor.

The stresses in planar cylindrical coordinates (i.e., $$\sigma_{rr}$$, $$\sigma_{\theta\theta}$$, and $$\sigma_{r\theta}$$) can be calculated from Cartesian stresses (i.e., $$\sigma_{x}$$, $$\sigma_{y}$$ and $$\gamma_{xy}$$) using standard coordinate transformations, for example

$$
\large \sigma_{rr}=\sigma_x\cos^2\theta+\sigma_y\sin^2\theta+\sigma_{xy}2\sin\theta\cos\theta
$$

(16)

$$
\large \sigma_{\theta\theta}=\sigma_x\sin^2\theta+\sigma_y\cos^2\theta-\sigma_{xy}2\sin\theta\cos\theta
$$

(17)

In this lab, you will measure displacements and strains in a polypropylene test specimen (Figure 6) with a circular cutout subject to tension. The DIC system will enable us to visualize the distribution of strains around the hole and observe the stress and strain concentration.

![](https://368320314-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-MIV0GglxIUR4tETuwA2%2F-MSzUGlPeLTx82VC5vnX%2F-MSzVERQch1PWB-Fz5J-%2Fimage.png?alt=media\&token=da7381be-8b2b-4ff5-a16b-e0c1b5e27088)

> **Figure 4**. Photograph of test specimen with hole.

## Procedure

### Specimen Preparation

A critically important step for a DIC experiment is to prepare the specimen's surface and to apply a speckle pattern that the software can interpret and transform into a strain field. Various resources such as [Trilion's FAQ](https://faq.trilion.com/docs/how-do-i-pattern-my-specimens/?seq_no=2) and [Correlated Solution's technical article](https://correlated.kayako.com/article/38-speckle-pattern-fundamentals) detail how best to do this. For this lab, the specimens have already been prepared, so the steps below are for your enlightenment.

#### Printed label method

If your specimen has a flat surface and good adhesion, self-adhesive labels with pre-printed speckle patterns can be directly applied to the specimen.  The following process was followed to generate speckles for this lab:

1. Download the [Correlated Solutions Speckle Generator](https://correlated.kayako.com/article/7-speckle-generator) software.
2. Apply the following settings before exporting to PDF (the geometry can change, but this is set up specifically for Dymo Extra Large shipping labels using a LabelWrite 4XL thermal printer):\
   ![](https://368320314-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F-MIV0GglxIUR4tETuwA2%2Fuploads%2F1z20WJDKL3i3fhNNZN4e%2Fimage.png?alt=media\&token=6d924a54-a363-477c-80e4-b14e2b0dd1c0)
3. Convert the PDF to a high-resolution image using [Adobe Acrobat Online](https://www.adobe.com/acrobat/online/pdf-to-jpg.html) or similar. This file can also be found below this list.
4. Open Dymo Connect, set up the Extra Large shipping label in portrait, and import the image from the previous step, scaling it up to full size.
5. Print labels.
6. Remove any previous labels and/or any large residues or deposits on the specimen surface.
7. Degrease the specimen's surface.
8. Carefully apply the label in the region of interest without folding the edges, and applying firm pressure to aid its adhesion.
9. Use a sharp knife to trim away the excess label, taking care to not cut away any from the region of interest.

{% file src="https://368320314-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F-MIV0GglxIUR4tETuwA2%2Fuploads%2F7GeHExq5eSBfZJi1872b%2FSpeckle3_0p02_80pc_81pc_4_6.png?alt=media&token=3c2870cb-dfe7-4c6e-bdc9-11758dce9513" %}
Image to be imported into Dymo Connect (speckle generator settings in filename)
{% endfile %}

{% file src="https://368320314-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F-MIV0GglxIUR4tETuwA2%2Fuploads%2F9t8ZfKUY4pfmz9VUo3JC%2FSpeckle3_0p02_80pc_81pc_4_6.dymo?alt=media&token=6fb9e499-4185-479c-b5c1-3b1f79782377" %}
Dymo Connect file ready to print on a Dymo LabelWriter 4XL using Extra Large shipping labels (4 x 6")
{% endfile %}

#### Paint-and-toothbrush method

For certain surfaces, such as those that aren't flat, speckling paint directly onto the specimen is the preferred approach. One such paint application method is using a toothbrush as follows:

* Lightly sand and deburr the specimen to remove any manufacturing artifacts. Wipe clean the specimen to remove any oils/residues that may prevent paint adhesion.
* Apply a matte white paint base layer to the specimen to remove any reflectivity it inherently has. Do this using spray paint, shaking the can well and applying in multiple thin layers with ample time for each layer to dry before applying the next.
* Dip a toothbrush into black paint, tapping off any excess. Having determined the appropriate distance away from the specimen to get the desired particle size beforehand, flick the brush's bristles to create a distribution of speckles over the base layer that will give good results. Consult the DIC manual for recommended particle size and coverage.

### DIC System Hardware Setup

1. Take a look at the tripod and ensure the legs are resting on the 3 X's marked on the floor
2. Visually inspect the camera and ensure it is facing the Instron machine with no yaw or pitch offset. This is VERY important since this is a 2D DIC system which cannot characterize out-of-plane displacements!
3. Ensure that the LED light power cord is plugged into the power strip.&#x20;
4. Plug the USB cable from the Camera into the USB 3.0 port on the front of the computer. A small green light will illuminate on the back of the camera once you plug this cable in.
5. <mark style="color:red;">**!! IF ANYTHING IS AWRY, DO NOT FIX IT YOURSELF. ASK YOUR TA FOR HELP !!**</mark>&#x20;
   1. _TA Note: Ask the Lab Manager or Head TA for assistance if necessary._
6. <mark style="color:red;">**!! BE VERY CAREFUL NOT TO BUMP OR KNOCK THE CAMERA OR TRIPOD AROUND !!**</mark>
   1. It is best to load all specimens into the Instron machine from BEHIND the Instron machine.
7. Turn on the Instron Machine and the Instron PC if it is not already turned on.
8. Open Bluehill Universal and ensure the Software connects to the Machine.

### Four-Point Bending Test

|               | Value |
| ------------- | ----- |
| _**a**_ (in.) | 4     |
| _**s**_ (in.) | 4     |
| _**L**_ (in.) | 12    |

> **Table 1.** Four-point loading parameters to be used in experiment (defined in Figure 2)

1. **Prepare the specimen**:
   1. Rotate the Instron grips such that it is facing forward if necessary. You will need 2 people to do this and **make sure a TA is supervising this process!**
   2. Place the 4 point bending fixture into the Instron grips. You will need 2 people to do this and **make sure a TA is supervising this process!**
      1. Grip the bending fixture such that the grip section on the fixture is flush to the back of the clamps. If done correctly, there should be a gap in the front.
      2. It should also be gripped \~3mm below where the grip starts to diverge. See the image below for reference.&#x20;
      3. Ensure that the front of the fixture is facing forward--The side labeled "Front"\
         ![](https://368320314-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F-MIV0GglxIUR4tETuwA2%2Fuploads%2F9ue3xkr1NSfFLgrlfU7w%2Fimage.png?alt=media\&token=83c3bd22-12ad-49db-819c-4d2b945999d0)
   3. Locate the beam specimen that has a self-adhesive speckle pattern label applied.
   4. Measure the thickness and width of the beam specimen being careful not to touch the speckle pattern with your fingers
   5. With the help of a TA, ensure that there is no folding, fading, or any other damage to the speckle pattern. If there is, apply a new speckle pattern sticker to the specimen.
   6. With the help of a TA, position the beam in the test fixture using a 12-inch lower support length and a 4-inch upper support length.&#x20;
      1. Place the rollers in locations to produce the four-point bending parameters listed in Table 1. There are arrows on the fixture itself to depict where the rollers must be placed
      2. Ensure the bottom rollers are on placed below the beam. These 2 rollers are labeled with a "B"
      3. Ensure the top rollers are placed above the beam. These 2 rollers are labeled with a "T"
      4. Ensure the letter "F" on all 4 rollers is facing the cameras. Furthermore, ensure all 4 rollers are flush to the front surface of the fixture. See the image below\
         ![](https://368320314-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F-MIV0GglxIUR4tETuwA2%2Fuploads%2FzhXRXB1GTv9iMQKo1epI%2Fimage.png?alt=media\&token=1ce6178e-d553-4bea-8cd0-b1373b641e11)
      5. Place the beam on the rollers such that the front face of the beam is resting just behind the line drawn on the rollers. Use the lines on the bottom rollers to do this. See the image below\
         ![](https://368320314-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F-MIV0GglxIUR4tETuwA2%2Fuploads%2FY3m18PslymfsFfxjJ1QQ%2Fimage.png?alt=media\&token=567344be-26f0-4876-83c1-b06025cc7e3e)
   7. **TA Note: If this line starts to become faded, redraw it with the sharpie in the green toolbox at the end of the lab.**
   8. Jog the Instron Crosshead down until there is very little play in the top rollers.
      1. You should use the fine adjustment wheel once you get very close to ensure you are not accidentally loading the specimen.&#x20;
      2. **BE CAREFUL NOT TO PINCH YOUR FINGERS DURING THIS PROCESS!!!!**
      3. A good way to do this is to zero the load and stop and scroll the fine adjustment wheel back up AS SOON as you see a load being applied.
      4. Another option is to use your fingers but again, be careful not to pinch your fingers.
   9. Zero the load and displacement on the Instron software.
2. **Verify LED Illumination:**
   1. Switch on the left side LED light by flipping the switch. Check to make sure it is illuminating the area of interest.&#x20;
   2. Switch off the left side LED.
   3. Switch on the right side LED light by flipping the switch. Check to make sure it is illuminating the area of interest.&#x20;
   4. If both LEDs are pointing in the right direction, turn on both lights and keep them on.
   5. <mark style="color:red;">**!! IF ANYTHING IS AWRY, DO NOT FIX IT YOURSELF. ASK YOUR TA FOR HELP !!**</mark>&#x20;
      1. _TA Note: Ask the Lab Manager or Head TA for assistance if necessary._
3. **Perform the experiment:**
   1. Open Vic-Snap 10 from the Start Menu
   2. Under Project Path, select a save location that is convenient and easy to access.&#x20;
   3. Under Speckle prefix, type in "4pt" and under Calibration prefix, type in "4pt-cal"
   4. Click OK. The software will open to the main screen.
   5. You should now see the specimen on your screen.&#x20;
   6. If needed, **HAVE A TA** raise or lower the tripod with the hand crank.
   7. On the bottom of the screen, you should see a slide rule where you can change the exposure time of the photograph. Slide this back and forth until you see no overexposure on the picture.
      1. You can see overexposure when you see red dots on the image.&#x20;
      2. Your goal is to get as much exposure as possible without ANY overexposure ANYWHERE on the image. You may have balance this a little bit--it is better to be _slightly_ underexposed instead of overexposed. Your TAs can help with this.
   8. When you are satisfied, click the "Focus" button on the top of the toolbar.
      1. Verify that the predicted noise is below 0.05.
      2. The camera has already been focused for you. If any changes are necessary, have your TA call the Lab Manager or Head TA for assistance.
      3. Unclick the "Focus" button.
      4. You are now ready to begin taking images.&#x20;
   9. Under Project on the left side of the screen, select the "Calibration" radio button.
      1. This is the radio button directly underneath "Speckle"
      2. Be sure not to select the Calibration tab!&#x20;
   10. Click the "Capture" button from the top toolbar.
   11. Under Project and Under System on the left side of the screen, switch back to the "Images" tab. You should now see a number 1 next to Calibration indicating you have taken you calibration photograph
   12. Select the "Speckle" radio button.
   13. Take a reference image of the specimen WITHOUT any loading by clicking "Capture" from the top toolbar. Your count of Speckle photographs should now read 1.
   14. Jog the Instron down using the fine adjustment wheel until you've applied a bending load of 150 lbf.
   15. Click "Capture" from the top toolbar. Your count of Speckle photographs should now read 2.
   16. Unload the specimen
4. **Upload Images to Vic-2D:**
   1. Without, closing the Vic-Snap Software, open the Vic-2D 7 software from the start menu.
   2. From the Home page, select the "Calibration images" button.&#x20;
   3. Locate the folder in which you have saved your images, and select the "4pt-cal" TIF file you captured earlier
   4. Select "Speckle Images" button from the top toolbar (4th from the left)
   5. Select and upload the Reference image and Loaded image TIF files you took earlier using Vic-Snap
   6. On the left hand side under Project, you should now have 2 speckle images and one calibration image
   7. Ensure that the proper image is selected as your reference image. It will have a red arrow next to the image.
      1. If you are unsure which of your speckle images was the reference image, you can double click the image and see which one is under loading.
5. **Calibrate the Scale**
   1. In this step, we will be using the calibration image to understand the dimensions of the specimen. We will draw a line across the dimension of the specimen that we know. Using this information, the software will be able to calculate strain in the dimensions we are interested in rather than pixels.
   2. Click the "Calibrate Scale" button from the top toolbar (6th from the left)
      1. Scroll in as best you can to zoom into the picture and pan to the required area. You can also resize the entire window if needed.&#x20;
      2. Once you are satisfied with how far you are zoomed in, select the "Manually Select" button under Tools (2nd from the left)
      3. Holding the left click button on the mouse, drag a line across the entire width of the specimen
         1. HINT: this line needs to be perpendicular to the length of the specimen. Think of the best way you can make this line as close to perpendicular as you can!
         2. You can always redraw this line until you are satisfied
      4. Under Point distance, enter the width of the specimen (1 inch). Click OK to save this. If you get prompted that this is a short line, select "Yes"&#x20;
6. **Perform Displacement Analysis**
   1. You should see a box that says "Aoi tools" near the top left of your screen. If you don't see this, select "Aoi Editor" from the "Window" drop down menu at the top of the screen
   2. Select the "Create Rectangle" button under Aoi tools (2nd from the left)
   3. Highlight your area of interest. This should be an area between the two rollers where you expect to see pure bending. You should also select a VERY small portion (a sliver) of the black area outside of the speckle pattern to ensure you are capturing the specimen edge effects!
      1. You can delete and redo this as many times as you would like until you are satisfied with the area you select
   4. Under Aoi tools, select the "Create Starting Point" button (2nd from the right)
      1. Select a point somewhere within the area of interest.
   5. Keep the default Subset value of 29 and Steps value of 7
   6. Select the Green "Start Analysis" button from the top toolbar. Verify that the proper image is selected for your reference and that the loaded image is checked in the box below.&#x20;
   7. Also verify your output directory. Keep this the same as folder in which you saved your images so everything is in one place!
   8. Click "Run"
   9. You will see a preview of the analysis on the proceeding screen. Does it look like what you would expect to see? Click "Close"
   10. Now that you have run your displacement analysis, we can calculate strain using this displacement data and the calibration image we characterized earlier.
   11. Select the "Calculate Strain" button from the top toolbar (7th from the right)
   12. Ensure that both ".out" files are selected for your computation. Click "Preview"
       1. Does this look like what you would expect?
       2. Discuss!
   13. If you are satisfied with this preview and are confident that this looks like what you would expect, click "Start"
   14. Click "Close"
7. **Visualize your Results**
   1. Under the "Plot" drop down menu at the top of the screen, select "New Plot"
   2. Under "Plotting Tools" on the left hand side, make sure you are on the "Contour" tab
   3. Under "Project" on the left hand side, go to the "Data" tab. Double click your _loaded_ image.
   4. Under "Plotting Tools" on the left hand side again, change the variables between xx, yy, xy, and principal strains and observe all the plots. You can and should also observe displacements in all 3 cartesian directions
      1. Discuss what you see with your labmates!
      2. Take notes in your lab notebooks!
      3. Does this all make sense?
      4. Discuss with your TA
      5. Redo any portions of the procedure if needed
   5. If you are satisfied with your results, select the "Data" drop-down menu and under "Export" select "All Data"
   6. Make sure both of your ".out" files are selected and click "Export"
      1. You may select any file format that works for you. The default is a CSV and is what we recommend.

### Open-Hole Tension Test

1. **Prepare the specimen**:
   1. Rotate the Instron grips such that it is facing sideways if necessary. You will need 2 people to do this and **make sure a TA is supervising this process!**
   2. Locate the open-hole dog-bone specimen that has a self-adhesive speckle pattern label applied.
   3. Measure the specimen's thickness, width, and hole diameter.
   4. With the help of a TA, ensure that there is no folding, fading, or any other damage to the speckle pattern. If there is, apply a new speckle pattern sticker to the specimen.
   5. With the help of a TA, position the specimen in the clamping test fixture.
   6. Zero the load and displacement on the Instron software.
2. **Verify LED Illumination:**
   1. Switch on the left side LED light by flipping the switch. Check to make sure it is illuminating the area of interest.&#x20;
   2. Switch off the left side LED.
   3. Switch on the right side LED light by flipping the switch. Check to make sure it is illuminating the area of interest.&#x20;
   4. If both LEDs are pointing in the right direction, turn on both lights and keep them on.
   5. <mark style="color:red;">**!! IF ANYTHING IS AWRY, DO NOT FIX IT YOURSELF. ASK YOUR TA FOR HELP !!**</mark>&#x20;
      1. _TA Note: Ask the Lab Manager or Head TA for assistance if necessary._
3. **Perform the experiment:**
   1. Open Vic-Snap 10 from the Start Menu
   2. Under Project Path, select a save location that is convenient and easy to access.&#x20;
   3. Under Speckle prefix, type in "OpenHole" and under Calibration prefix, type in "OpenHole-cal"
   4. Click OK. The software will open to the main screen.
   5. You should now see the specimen on your screen.&#x20;
   6. If needed, **HAVE A TA** raise or lower the tripod with the hand crank.
   7. On the bottom of the screen, you should see a slide rule where you can change the exposure time of the photograph. Slide this back and forth until you see no overexposure on the picture.
      1. You can see overexposure when you see red dots on the image.&#x20;
      2. Your goal is to get as much exposure as possible without ANY overexposure ANYWHERE on the image.
   8. When you are satisfied, click the "Focus" button on the top of the toolbar.
      1. Verify that the predicted noise is below 0.05.
      2. The camera has already been focused for you. If any changes are necessary, have your TA call the Lab Manager or Head TA for assistance.
      3. Unclick the "Focus" button.
      4. You are now ready to begin taking images.&#x20;
   9. Under Project on the left side of the screen, select the "Calibration" radio button
      1. This is the radio button directly underneath "Speckle"
      2. Be sure not to select the Calibration tab!&#x20;
   10. Click the "Capture" button from the top toolbar.
   11. Under Project and Under System on the left side of the screen, switch back to the "Images" tab. You should now see a number 1 next to Calibration indicating you have taken you calibration photograph
   12. Select the "Speckle" radio button.
   13. Take a reference image of the specimen WITHOUT any loading by clicking "Capture" from the top toolbar. Your count of Speckle photographs should now read 1.
   14. Jog the Instron crosshead up using the fine adjustment wheel until you've applied a tensile load of 2.2 kN.
   15. Click "Capture" from the top toolbar. Your count of Speckle photographs should now read 2.
   16. Unload the specimen
4. **Upload Images to Vic-2D:**
   1. Without, closing the Vic-Snap Software, open the Vic-2D 7 software from the start menu.
   2. From the Home page, select the "Calibration images" button.&#x20;
   3. Locate the folder in which you have saved your images, and select the "OpenHole-cal" TIF file you captured earlier
   4. Select "Speckle Images" button from the top toolbar (4th from the left)
   5. Select and upload the Reference image and Loaded image TIF files you took earlier using Vic-Snap
   6. On the left hand side under Project, you should now have 2 speckle images and one calibration image
   7. Ensure that the proper image is selected as your reference image. It will have a red arrow next to the image.
      1. If you are unsure which of your speckle images was the reference image, you can double click the image and see which one is under loading.
5. **Calibrate the Scale**
   1. In this step, we will be using the calibration image to understand the dimensions of the specimen. We will draw a line across the dimension of the specimen that we know. Using this information, the software will be able to calculate strain in the dimensions we are interested in rather than pixels.
   2. Click the "Calibrate Scale" button from the top toolbar (6th from the left)
      1. Scroll in as best you can to zoom into the picture and pan to the required area. You can also resize the entire window if needed.&#x20;
      2. Once you are satisfied with how far you are zoomed in, select the "Manually Select" button under Tools (2nd from the left)
      3. Holding the left click button on the mouse, drag a line across the entire width of the specimen
         1. HINT: this line needs to be perpendicular to the length of the specimen. Think of the best way you can make this line as close to perpendicular as you can!
         2. You can always redraw this line until you are satisfied
      4. Under Point distance, enter the width of the specimen (1.5 inches). Click OK to save this. If you get prompted that this is a short line, select "Yes"&#x20;
6. **Perform Displacement Analysis**
   1. You should see a box that says "Aoi tools" near the top left of your screen. If you don't see this, select "Aoi Editor" from the "Window" drop down menu at the top of the screen
   2. Select the "Create Rectangle" button under Aoi tools (2nd from the left)
   3. Highlight your area of interest. You should select the area around the open hole all the way to the edge of the specimen.&#x20;
      1. Select a vertical length that is about 1.5x the width of the dogbone specimen, creating a rectangle
      2. You should also select a VERY small portion (a sliver) of the black area outside of the speckle pattern to ensure you are capturing the specimen edge effects!
      3. You can delete and redo this as many times as you would like until you are satisfied with the area you select
   4. Select the "Cut Circle" button under Aoi tools (3rd from the right)
      1. Cut out dark section of the hole MAKING SURE you are not cutting out any part of the specimen itself!
   5. If necessary, select a starting point by clicking "Select Starting Point" under Aoi tools (2nd from the right).
   6. Keep the default Subset value of 29 and Steps value of 7
   7. Select the Green "Start Analysis" button from the top toolbar. Verify that the proper image is selected for your reference and that the loaded image is checked in the box below.&#x20;
   8. Also verify your output directory. Keep this the same as folder in which you saved your images so everything is in one place!
   9. Click "Run"
   10. You will see a preview of the analysis on the proceeding screen. Does it look like what you would expect to see? Click "Close"
   11. Now that you have run your displacement analysis, we can calculate strain using this displacement data and the calibration image we characterized earlier.
   12. Select the "Calculate Strain" button from the top toolbar (7th from the right)
   13. Ensure that both ".out" files are selected for your computation. Click "Preview"
       1. Does this look like what you would expect?
       2. Discuss!
   14. If you are satisfied with this preview and are confident that this looks like what you would expect, click "Start"
   15. Click "Close"
7. **Visualize your Results**
   1. Under the "Plot" drop down menu at the top of the screen, select "New Plot"
   2. Under "Plotting Tools" on the left hand side, make sure you are on the "Contour" tab
   3. Under "Project" on the left hand side, click the "Data" tab. Double click your _loaded_ image.
   4. Under "Plotting Tools" on the left hand side again, change the variables between xx, yy, xy, and principal strains and observe all the plots. You can and should also observe displacements in all 3 cartesian directions
      1. Discuss what you see with your labmates!
      2. Take notes in your lab notebooks!
      3. Does this all make sense?
      4. Discuss with your TA
      5. Redo any portions of the procedure if needed
   5. If you are satisfied with your results, select the "Data" drop-down menu and under "Export" select "All Data"
   6. Make sure both of your ".out" files are selected and click "Export"
      1. You may select any file format that works for you. The default is a CSV and is what we recommend.

### &#x20;**Shutdown Procedure**

1. <mark style="color:red;">**CHECK YOUR DATA FILES. REDO ANY PORTIONS OF THE LAB YOU FEEL YOU MUST REDO**</mark>
2. Close the Vic-2D and Vic-Snap softwares. You may save the project to your folder in Vic-2D if you wish but it is not necessary
3. Turn off both the LED lights by flipping the switches.
4. Remove the specimens from the Instron Machine and place them on the Table for the next groups.
5. Unplug the Camera USB cable from the front of the computer.
6. Have your TA upload your data to Canvas. It is best to zip your entire folder containing all your images, output files, and exported data files

## Data to be Taken

1.  Thickness and width of the beam, and load value used in the four-point bending test.

    ​
2.  Displacement and strain data from the VIC-2D software for the four-point bending test.

    ​
3.  Thickness and width of the specimen, hole diameter, and load value used in the open-hole tension test.

    ​
4.  Displacement and strain data from the VIC-2D software for the open-hole tension test.

    ​

## ​Data Reduction

1. Using a best linear fit for the appropriate region of your $$\varepsilon_x(y)$$ plots from the four-point bending test, compute the slope ($$\kappa$$) and intercept (_b_) relative to a coordinate axis centered on your specimen.
2. From your experimental data, determine the tensile and compressive moduli ($$E_T$$ _and_ $$E_C$$) for polypropylene.
3. From your plots of transverse normal strain $$\varepsilon_y$$ divided by the axial strain $$\varepsilon_x$$, determine a value for Poisson’s ratio ($$\nu$$) for polypropylene.
4. For the open-hole tension test, compute the stresses in your specimen based on the measured strains and the appropriate _measured_ modulus of elasticity for polypropylene.

## Results Needed for Data Report

1. Table of beam dimensions and load value used in the four-point bending test.
2. Table of specimen dimensions, hole size and load value used in the open-hole tension test.
3. “Image graphs” or “full-field color plots”$$^1$$ of the axial (horizontal) and transverse (vertical) displacement field for the field of view analyzed by the VIC-2D software in the bending test. Choose your color scaling wisely to accentuate any important gradients. Be sure to also include color bars showing how your colors map to the values of displacement.

{% hint style="info" %}
$$^1$$Here an “image” means a false-color image, where each displacement (or strain) measurement location is like a pixel in the false-color image, and the color of the pixel corresponds to the value being shown (axial displacement in this case). You can do this, for example, with the image function in Matlab
{% endhint %}

4. Images of $$\varepsilon_x$$, $$\varepsilon_y$$ and $$\gamma_{xy}$$ for the field of view imaged and analyzed by the VIC-2D software in the bending test, with color bars.
5. For the four-point bending test, plots of the axial and transverse normal strain fields as a function of _y_ (with the y-axis as defined in Figure 5), at three axial locations between the two inner load points (i.e., within the constant moment region). One of these should be the center axial location.

![](https://368320314-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2Fae3610%2F-MMHuyGav47Xk9URWn6t%2F-MMHxvUXLBSOvKnUYqdO%2F19.jpeg?generation=1605562253061831\&alt=media)

> **Figure 5.** Through-thickness stress-strain distribution for material with different moduli in compression and tension.

6. For the bending test, plot of the transverse normal strain $$\varepsilon_y$$ divided by the axial strain $$\varepsilon_x$$ along the center line used for Result 5.
7. Table of measured values of $$\kappa$$, _b,_ and the polypropylene properties $$E_T$$, $$E_C$$, and $$\nu$$. Include in your table the published values for the polypropylene properties (include your source for those values).
8. Images of the axial strain ($$\varepsilon_x$$) and transverse strain ($$\varepsilon_y$$) fields for the region analyzed by the VIC-2D software in the open-hole tension test, with color bars.
9. Images of the axial ($$\sigma_x$$) and transverse stress ($$\sigma_y$$) fields based on your measured strains and measured modulus of polypropylene, with color bars for the open hole tension test.
10. Images of the normal radial stress ($$\sigma_{rr}$$) and normal tangential stress ($$\sigma_{\theta\theta}$$) fields for the open-hole tension tests, with color bars.
11. A single graph containing plots of the tangential stress along a line perpendicular to the length dimension of your specimen that passes through the center of the hole for the open hole tension test.
12. A single graph containing a plot of the tangential stress (normalized by its value far from the hole) as a function of angle around the hole, close to the edge of hole.
