Effective development of advanced materials and components requires an understanding of their behavior under load in an application. Optical full-field measurement techniques are increasingly being used in material testing, fracture mechanics, and vibration analysis. Digital image correlation (DIC), for example, is a full-field image analysis method that uses grey-value digital images to determine the contour and displacements in three dimensions for an object under load. Rapid new developments in high-resolution digital cameras have increased their utility for static and dynamic DIC applications. Our research has focused on developing a modular analysis system, including all of the components needed to achieve reliable and accurate measurements in an industrial setting.
General descriptions of optical systems for 3D measurements in experimental applications are reported in the literature (Sutton,1 Mguil-Touchal,2 Winter3). Because DIC systems must be calibrated to get accurate results, we developed an improved calibration procedure designed for ease of use, reliability, and fast calibration. In addition, our approach calculates uncertainty intervals for the calibration parameters, including contour, displacement, and strain. We developed modular software in order to allow for flexibility when selecting hardware for other applications.4
Our process uses a stereoscopic camera to image each point of the object on a specific pixel in the camera's image plane. Then, the coordinate of each point is calculated using the ‘intrinsic’ imaging parameters for each camera (focal length, principle point, and distortion parameters) and the ‘extrinsic parameters’ or orientations of the cameras with respect to each other (the rotation matrix and translation vector). Calculations are based on a pinhole imaging model.5
During the calibration process, images are taken of a calibration panel (see Figure 1). The corresponding markers on the panel are detected and displayed automatically on a monitor. Typically, eight images taken from different perspectives are enough to calculate all of the calibration parameters accurately. This visual, real-time procedure enables an easy, reliable, and fast calibration of the system.6
Figure 1. The setup of a measurement includes a calibration panel.
The correlation algorithm used to calculate the contour and the displacements of the object is based on tracking the grey value pattern G1(x,y) in small facets (see Figure 2). Facet coordinates (x,y) are transformed into (x1,y1) by assuming pseudo-affine mapping, which is a combination of translation, stretch, shear, and distortion components:6
Figure 2. The correlation process compares the grey value pattern with facet G1(left) and transformed grey value pattern with facet G2 (right).
Parameters are determined by minimizing the distance between the observed grey pattern G2(x,y) in the second image and the original pattern G1(x,y), and by applying the coordinate transformations (xt,yt) plus photogrammetric corrections to account for different contrast conditions and varying intensity levels of the images:
Typically, a series of up to several hundred images are acquired to test an object under static or dynamic load. Supporting various types of triggering (including single event, pre-/post event, or clock signal), the system automatically identifies the starting points in all of the images. The displacement accuracy of the correlation algorithm, typically about 0.01, is calculated for each point. Using a megapixel camera, a displacement resolution of 1/100.000 of the field of view can be achieved. Next, the displacements in the tangential direction are calculated using the 3D displacement and contour data. Finally, orthogonal, shear, and principal strain components are determined using the Lagrange strain definition.
In one application, we investigated the vibration of a 300 × 260mm rubber membrane placed in front of a loudspeaker emanating a frequency of 59.9Hz. For the image acquisition, highspeed cameras (Nanosense MK III) were used with resolution of 1280 × 1024 pixels. Figure 3 shows the calculated out-of-plane deformation when t = 70.410-3s (vibration began at t=0) and also the temporal displacement of the central point (using a frame rate of 625Hz).
Figure 3. The displayed data shows the full-field out-of-plane deformation of the membrane at minimum deflection in the center (top) and a temporal plot of the displacement of the center point (bottom).
Another application example studies a standard aluminium sample in a tensile test. Figure 4 illustrates the principal strain distribution before failure and the evolution of the principal strain at different spatial positions during the experiment.
Figure 4. In an aluminum tensile test, the software shows the evolution of principal strains for different spatial positions on the sample.
Improvements in calibration procedures can make DIC systems easier to use, reduce calibration times, and enhance reliability and accuracy of measurements. By taking a modular approach to hardware and software, we have made this system suitable for static as well as dynamic applications. The system includes convenient features for handling, evaluating, displaying, post-processing, and analysis of data.